Question

Give a example of 2$\times$2 matrix A such that A has one independent eigenvector while $A^2$ has two independent eigenvectors.

score 37 · Answer 1 · 2026-03-27 10:46:06

37

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Give a example of 2$\times$2 matrix A such that A has one independent eigenvector while $A^2$ has two independent eigenvectors.

Published on 27 Mar 2026 - 10:46

score 1.3k · Answer 2 · 2026-03-24 22:01:52

1.3k

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Upper triangular form is not sufficient to decide the rank of a matrix

Published on 24 Mar 2026 - 22:01

score 53 · Answer 3 · 2018-03-04 16:56:26

53

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Show that there exists this matrix (Jordan decomposition)

Published on 04 Mar 2018 - 16:56

score 69 · Answer 4 · 2026-03-29 22:44:19

69

Views

Solve the equation $\sin(\theta) + c\sin(2\theta) = 0$?

Published on 29 Mar 2026 - 22:44

score 16.6k · Answer 5 · 2018-03-04 17:50:51

16.6k

Views

Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.

Published on 04 Mar 2018 - 17:50

score 855 · Answer 6 · 2026-03-25 12:46:25

855

Views

Characteristic polynomial for the frobenious map.

Published on 25 Mar 2026 - 12:46

score 1.2k · Answer 7 · 2026-03-26 09:17:58

1.2k

Views

Do all polynomials of degree 2 form a subspace of $F(-\infty,\infty)$

Published on 26 Mar 2026 - 9:17

score 68 · Answer 8 · 2018-03-04 18:44:03

68

Views

Quaternions Basis Proof

Published on 04 Mar 2018 - 18:44

score 41 · Answer 9 · 2026-03-26 09:18:13

41

Views

Do functions $f$ in $F(-\infty,\infty)$ that satisfy $f(-x)=f(x)$ form a subspace of $F(-\infty,\infty)$?

Published on 26 Mar 2026 - 9:18

score 312 · Answer 10 · 2018-03-04 19:46:16

312

Views

How to find the matrix that represents a linear operator with respect to a given basis?

Published on 04 Mar 2018 - 19:46

score 116 · Answer 11 · 2026-04-03 19:57:03

116

Views

Relation for the determinant of a special Hadamard product.

Published on 03 Apr 2026 - 19:57

score 148 · Answer 12 · 2018-03-04 20:25:35

$A$ and $B$ are square complex matrices of the same size and $\text{rank}(AB − BA) = 1.$ Show that $(AB − BA)^2= 0.$

score 26 · Answer 13 · 2018-03-04 20:47:06

26

Views

Show there is a matrix satisfying this requirement(Jordan canonical form)

Published on 04 Mar 2018 - 20:47

score 289 · Answer 14 · 2026-03-25 11:13:45

289

Views

are permutation coordinate of a point linear independent under cyclic group with odd length?

Published on 25 Mar 2026 - 11:13

score 473 · Answer 15 · 2026-03-28 08:09:34

473

Views

Inferences made from $(T-2I)(T-3I)(T-4I)v = 0$

Published on 28 Mar 2026 - 8:09

List Question

Give a example of 2$\times$2 matrix A such that A has one independent eigenvector while $A^2$ has two independent eigenvectors.

Upper triangular form is not sufficient to decide the rank of a matrix

Show that there exists this matrix (Jordan decomposition)

Solve the equation $\sin(\theta) + c\sin(2\theta) = 0$?

Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.

Characteristic polynomial for the frobenious map.

Do all polynomials of degree 2 form a subspace of $F(-\infty,\infty)$

Quaternions Basis Proof

Do functions $f$ in $F(-\infty,\infty)$ that satisfy $f(-x)=f(x)$ form a subspace of $F(-\infty,\infty)$?

How to find the matrix that represents a linear operator with respect to a given basis?

Relation for the determinant of a special Hadamard product.

$A$ and $B$ are square complex matrices of the same size and $\text{rank}(AB − BA) = 1.$ Show that $(AB − BA)^2= 0.$

Show there is a matrix satisfying this requirement(Jordan canonical form)

are permutation coordinate of a point linear independent under cyclic group with odd length?

Inferences made from $(T-2I)(T-3I)(T-4I)v = 0$

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