Question

Suppose $A^n = 0$ matrix for some $n > 1$. Find an inverse for $I - A$.

score 1.6k · Answer 1 · 2026-04-13 04:00:13

1.6k

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Suppose $A^n = 0$ matrix for some $n > 1$. Find an inverse for $I - A$.

Published on 13 Apr 2026 - 4:00

score 147 · Answer 2 · 2026-04-12 03:48:40

147

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How can you divine (the trick of) multiplying both sides by $T - \lambda_k I$?

Published on 12 Apr 2026 - 3:48

score 411 · Answer 3 · 2026-03-29 10:49:11

411

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Union of finite linearly independent subsets of eigenspaces, is a lin-indep subset.

Published on 29 Mar 2026 - 10:49

score 93 · Answer 4 · 2014-05-16 20:48:21

93

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Does "a matrix of $L$ with respect to $\color{red}{\text{S and T}} \,$" signify $[L]_{T \leftarrow S}$ or $[L]_{S \leftarrow T}$?

Published on 16 May 2014 - 20:48

score 887 · Answer 5 · 2014-05-17 16:30:44

887

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When Dim eigenspace = 1, any $2\times 2$ complex matrix A is similar to $\left(\begin{array}{ll} \lambda & 1\\ 0 & \lambda \end{array}\right)$.

Published on 17 May 2014 - 16:30

score 4.4k · Answer 6 · 2026-04-13 04:06:24

4.4k

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Proof of Cayley-Hamilton Theorem for Diagonalisable Matrices [Lay P326 Ch 5 Sup Q7]

Published on 13 Apr 2026 - 4:06

score 22.7k · Answer 7 · 2026-04-09 18:14:17

22.7k

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How does this prove: All eigenvalues of a triangular matrix = All its diagonal entries?

Published on 09 Apr 2026 - 18:14

score 112 · Answer 8 · 2014-05-20 20:38:38

112

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2 x 2 Phase Portrait for 2 x 2 Linear System with Real Coefficients. Boyce, p395, Figure 7.5.4a

Published on 20 May 2014 - 20:38

score 2.1k · Answer 9 · 2026-04-07 14:59:32

2.1k

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For this 2 by 2 locally linear system, how to determine that this "indeterminate" critical point is a centre? Boyce, p516, Question 9.3.12

Published on 07 Apr 2026 - 14:59

score 307 · Answer 10 · 2026-03-25 21:31:31

307

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How to Complete Sketch of a function of two variables $ f(x, y) = 3x - x^3 - 2y^2 + y^4$ ? [Stewart P930 Question 14.7.4]

Published on 25 Mar 2026 - 21:31

score 1k · Answer 11 · 2026-04-13 02:01:50

1k

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Any $2\times 2$ complex matrix A is similar to one of these three: (See first line of the question)

Published on 13 Apr 2026 - 2:01

score 3k · Answer 12 · 2026-03-29 12:38:41

3k

Views

Same characteristic polynomial $\iff$ same eigenvalues?

Published on 29 Mar 2026 - 12:38

score 292 · Answer 13 · 2026-04-12 21:09:57

292

Views

An explanation for a Jordan normal form proof from the Kaye and Wilson book

Published on 12 Apr 2026 - 21:09

score 92 · Answer 14 · 2026-04-12 10:05:04

92

Views

Confused About Step in Proof of Divergence of $\sum \frac{1}{p}$

Published on 12 Apr 2026 - 10:05

score 1.5k · Answer 15 · 2014-06-01 07:02:02

1.5k

Views

Proof of k'th power theorem: $x^k \equiv a \pmod n$ has a solution $\iff$ $a^{\phi(n)/\gcd(k, \phi(n))} \equiv 1 \pmod n$.

Published on 01 Jun 2014 - 7:02

List Question

Suppose $A^n = 0$ matrix for some $n > 1$. Find an inverse for $I - A$.

How can you divine (the trick of) multiplying both sides by $T - \lambda_k I$?

Union of finite linearly independent subsets of eigenspaces, is a lin-indep subset.

Does "a matrix of $L$ with respect to $\color{red}{\text{S and T}} \,$" signify $[L]_{T \leftarrow S}$ or $[L]_{S \leftarrow T}$?

When Dim eigenspace = 1, any $2\times 2$ complex matrix A is similar to $\left(\begin{array}{ll} \lambda & 1\\ 0 & \lambda \end{array}\right)$.

Proof of Cayley-Hamilton Theorem for Diagonalisable Matrices [Lay P326 Ch 5 Sup Q7]

How does this prove: All eigenvalues of a triangular matrix = All its diagonal entries?

2 x 2 Phase Portrait for 2 x 2 Linear System with Real Coefficients. Boyce, p395, Figure 7.5.4a

For this 2 by 2 locally linear system, how to determine that this "indeterminate" critical point is a centre? Boyce, p516, Question 9.3.12

How to Complete Sketch of a function of two variables $ f(x, y) = 3x - x^3 - 2y^2 + y^4$ ? [Stewart P930 Question 14.7.4]

Any $2\times 2$ complex matrix A is similar to one of these three: (See first line of the question)

Same characteristic polynomial $\iff$ same eigenvalues?

An explanation for a Jordan normal form proof from the Kaye and Wilson book

Confused About Step in Proof of Divergence of $\sum \frac{1}{p}$

Proof of k'th power theorem: $x^k \equiv a \pmod n$ has a solution $\iff$ $a^{\phi(n)/\gcd(k, \phi(n))} \equiv 1 \pmod n$.

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