List questions from matrix-rank

Published on 19 May 2020 - 2:02

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Prove that a non-zero vector cannot belong to the rowspace and nullspace of a matrix at the same time.

Published on 19 May 2020 - 10:27

159

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Some use this matrix to disprove that the number of eigenvalues is equal to rank.

Published on 20 May 2020 - 6:31

202

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Lower Bound on Rank of a Boolean Matrix

Published on 20 May 2020 - 15:05

457

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Why does adding $\lambda \boldsymbol{I}$ to $\boldsymbol{X}^T\boldsymbol{X}$ for $\lambda > 0$ guarantee invertibility?

Published on 21 May 2020 - 23:04

573

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Pseudoinverse of block diagonal matrix

Published on 26 Mar 2026 - 9:39

80

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Design a positive integral matrix that isn't full rank

Published on 23 Feb 2026 - 8:39

249

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Different rank and nullity obtained from intuition and computation

Published on 26 May 2020 - 17:11

550

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How does the linear independence or dependence of the set of column vectors of a matrix depend on that of the set of row vectors of the same?

Published on 28 May 2020 - 9:38

29

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Rank of a left-orthogonal decomposition $A^T=UB^T$

Published on 31 May 2020 - 14:44

62

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Eigenvalues and rank connection

Published on 31 May 2020 - 15:43

327

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Rank of some power of a given matrix

Published on 31 May 2020 - 19:14

793

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Symmetric Matrix over a finite field of Characteristic 2

Published on 02 Jun 2020 - 18:43

194

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What can you say about $T$ if dim$(V) =$ Rank$(T - \lambda I)$?

Published on 02 Jun 2020 - 21:43

195

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Accuracy of low rank approximation

Published on 03 Jun 2020 - 21:14

List Question

Matrix-Matrix Multiplication Properties

Prove that a non-zero vector cannot belong to the rowspace and nullspace of a matrix at the same time.

Some use this matrix to disprove that the number of eigenvalues is equal to rank.

Lower Bound on Rank of a Boolean Matrix

Why does adding $\lambda \boldsymbol{I}$ to $\boldsymbol{X}^T\boldsymbol{X}$ for $\lambda > 0$ guarantee invertibility?

Pseudoinverse of block diagonal matrix

Design a positive integral matrix that isn't full rank

Different rank and nullity obtained from intuition and computation

How does the linear independence or dependence of the set of column vectors of a matrix depend on that of the set of row vectors of the same?

Rank of a left-orthogonal decomposition $A^T=UB^T$

Eigenvalues and rank connection

Rank of some power of a given matrix

Symmetric Matrix over a finite field of Characteristic 2

What can you say about $T$ if dim$(V) =$ Rank$(T - \lambda I)$?

Accuracy of low rank approximation

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