# OCME · Knowledge & practice explorer

302 MKO / 1,441 families / 360 batches / 36,000 questions.

36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training.

25 results; page 1/1.

## Question 16476: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0026`; number: 16476
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0026/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0026/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0026.json)

## Question 16477: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0027`; number: 16477
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0027/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0027/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0027.json)

## Question 16478: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0028`; number: 16478
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0028/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0028/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0028.json)

## Question 16479: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0029`; number: 16479
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0029/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0029/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0029.json)

## Question 16480: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0030`; number: 16480
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0030/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0030/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0030.json)

## Question 16481: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0031`; number: 16481
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0031/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0031/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0031.json)

## Question 16482: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0032`; number: 16482
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0032/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0032/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0032.json)

## Question 16483: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0033`; number: 16483
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0033/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0033/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0033.json)

## Question 16484: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0034`; number: 16484
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0034/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0034/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0034.json)

## Question 16485: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0035`; number: 16485
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0035/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0035/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0035.json)

## Question 16486: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0036`; number: 16486
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0036/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0036/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0036.json)

## Question 16487: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0037`; number: 16487
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0037/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0037/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0037.json)

## Question 16488: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0038`; number: 16488
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0038/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0038/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0038.json)

## Question 16489: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0039`; number: 16489
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0039/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0039/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0039.json)

## Question 16490: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0040`; number: 16490
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0040/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0040/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0040.json)

## Question 16491: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0041`; number: 16491
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0041/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0041/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0041.json)

## Question 16492: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0042`; number: 16492
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0042/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0042/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0042.json)

## Question 16493: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0043`; number: 16493
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0043/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0043/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0043.json)

## Question 16494: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0044`; number: 16494
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0044/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0044/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0044.json)

## Question 16495: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0045`; number: 16495
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0045/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0045/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0045.json)

## Question 16496: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0046`; number: 16496
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0046/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0046/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0046.json)

## Question 16497: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0047`; number: 16497
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0047/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0047/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0047.json)

## Question 16498: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0048`; number: 16498
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0048/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0048/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0048.json)

## Question 16499: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0049`; number: 16499
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0049/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0049/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0049.json)

## Question 16500: A Homogeneous Kernel Has Universal Closure under Real Linear Combinations

- ID: `q-20261014-advance-20261101-r01-vector-subspace-0050`; number: 16500
- Processing: second_context_reviewed
- MKO: [mko-vector-subspace](/en/mko/mko-vector-subspace/)
- Family: [qf-mod32-subspace-universal-line-certificate](/en/explore/?family=qf-mod32-subspace-universal-line-certificate)
- Batch: [batch-20261014-advance-20261101-r01-vector-subspace-foundations](/en/explore/?batch=batch-20261014-advance-20261101-r01-vector-subspace-foundations)
- [Derivation](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0050/) / [Markdown](/en/questions/q-20261014-advance-20261101-r01-vector-subspace-0050/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261101-r01-vector-subspace-0050.json)