Question

If $a$ is an integer, $A=\begin{bmatrix}a+1&2\\-1&a-2\end{bmatrix},\quad P=\begin{bmatrix}1&2\\-1&-1\end{bmatrix},\quad Q=PAP$, Find $P^2$ and $Q$

score 88 · Answer 1 · 2026-03-24 22:07:47

88

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If $a$ is an integer, $A=\begin{bmatrix}a+1&2\\-1&a-2\end{bmatrix},\quad P=\begin{bmatrix}1&2\\-1&-1\end{bmatrix},\quad Q=PAP$, Find $P^2$ and $Q$

Published on 24 Mar 2026 - 22:07

score 83 · Answer 2 · 2026-03-22 20:37:39

83

Views

degree of $P(x)$ , the minimal polynomial of $A$

Published on 22 Mar 2026 - 20:37

score 512 · Answer 3 · 2018-02-23 13:31:53

512

Views

Eigenvalues of a sum of power of a matrix

Published on 23 Feb 2018 - 13:31

score 40 · Answer 4 · 2018-02-23 20:01:27

40

Views

$A$ is similar to a triangular matrix but not $A$ need not be diagonalisable matrix.

Published on 23 Feb 2018 - 20:01

score 114 · Answer 5 · 2026-03-25 06:12:42

114

Views

Similarity of $3\times3$ matrices via Jordan canonical form

Published on 25 Mar 2026 - 6:12

score 102 · Answer 6 · 2018-02-24 15:18:50

102

Views

Eigenvalues of block matrix with similar rows

Published on 24 Feb 2018 - 15:18

score 195 · Answer 7 · 2018-02-24 18:17:30

195

Views

The characteristic values of the p-th compound matrix

Published on 24 Feb 2018 - 18:17

score 95 · Answer 8 · 2018-02-24 20:44:44

95

Views

Upper bound of smallest eigenvalue of a structure tensor matrix

Published on 24 Feb 2018 - 20:44

score 89 · Answer 9 · 2026-03-24 22:09:44

89

Views

What is the mistake in my matrix power formula?

Published on 24 Mar 2026 - 22:09

score 430 · Answer 10 · 2018-02-24 21:42:48

430

Views

Eigenvalue and Eigenvector of $\small\pmatrix{0 & 0 \\ 0 & -7}$

Published on 24 Feb 2018 - 21:42

score 252 · Answer 11 · 2026-03-22 16:11:45

252

Views

Spectrum of tridiagonal block matrix

Published on 22 Mar 2026 - 16:11

score 292 · Answer 12 · 2018-02-25 04:12:48

292

Views

Form of a matrix in a basis where some of the basis vectors are eigenvectors

Published on 25 Feb 2018 - 4:12

score 7.3k · Answer 13 · 2026-03-25 11:17:15

7.3k

Views

$ST$ and $TS$ have the same eigenvalues.

Published on 25 Mar 2026 - 11:17

score 200 · Answer 14 · 2026-03-26 17:14:35

200

Views

What is the "Geometric Series Trick" and how is it applied here during the convergence proof of the Rayleigh Quotient Iteration?

Published on 26 Mar 2026 - 17:14

score 121 · Answer 15 · 2026-03-25 09:40:00

121

Views

Orthogonality of eigenvectors of a positive operator in the polar decomposition

Published on 25 Mar 2026 - 9:40

List Question

If $a$ is an integer, $A=\begin{bmatrix}a+1&2\\-1&a-2\end{bmatrix},\quad P=\begin{bmatrix}1&2\\-1&-1\end{bmatrix},\quad Q=PAP$, Find $P^2$ and $Q$

degree of $P(x)$ , the minimal polynomial of $A$

Eigenvalues of a sum of power of a matrix

$A$ is similar to a triangular matrix but not $A$ need not be diagonalisable matrix.

Similarity of $3\times3$ matrices via Jordan canonical form

Eigenvalues of block matrix with similar rows

The characteristic values of the p-th compound matrix

Upper bound of smallest eigenvalue of a structure tensor matrix

What is the mistake in my matrix power formula?

Eigenvalue and Eigenvector of $\small\pmatrix{0 & 0 \\ 0 & -7}$

Spectrum of tridiagonal block matrix

Form of a matrix in a basis where some of the basis vectors are eigenvectors

$ST$ and $TS$ have the same eigenvalues.

What is the "Geometric Series Trick" and how is it applied here during the convergence proof of the Rayleigh Quotient Iteration?

Orthogonality of eigenvectors of a positive operator in the polar decomposition

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