Question

Let $T, N :V \to V$, N is nilpotent, T is invertible and $NT = TN$. Prove $N+T$ invertible.

score 134 · Answer 1 · 2026-04-16 11:21:07

134

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Let $T, N :V \to V$, N is nilpotent, T is invertible and $NT = TN$. Prove $N+T$ invertible.

Published on 16 Apr 2026 - 11:21

score 4.9k · Answer 2 · 2026-04-11 13:02:26

4.9k

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Solving least squares problem using partial derivatives

Published on 11 Apr 2026 - 13:02

score 1.3k · Answer 3 · 2026-04-15 20:49:57

1.3k

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Here is my proof that the elementary $k$-forms form a basis for $A^k{(\mathbb{R}^n)}$. Is this correct?

Published on 15 Apr 2026 - 20:49

score 75 · Answer 4 · 2026-04-23 18:13:34

75

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Getting vectors and eigenvalue from an eigenvector problem

Published on 23 Apr 2026 - 18:13

score 265 · Answer 5 · 2026-04-10 05:29:17

265

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Prove that $T$ is a positive definite operator

Published on 10 Apr 2026 - 5:29

score 106 · Answer 6 · 2026-04-13 20:56:38

106

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Exercise on degree extensions of quadratic subfield over $\Bbb Q$

Published on 13 Apr 2026 - 20:56

score 2.8k · Answer 7 · 2026-04-12 23:45:10

2.8k

Views

Find the vector in w in W closest to v.

Published on 12 Apr 2026 - 23:45

score 538 · Answer 8 · 2026-04-13 16:14:02

538

Views

Let T1 be the linear transformation corresponding to a counterclockwise rotation of 120 degrees

Published on 13 Apr 2026 - 16:14

score 132 · Answer 9 · 2026-04-11 08:57:03

132

Views

Merton 1972 efficiency frontier solution using linear algebra

Published on 11 Apr 2026 - 8:57

score 838 · Answer 10 · 2026-04-14 11:01:46

838

Views

Characteristic polynomial of operator is the product of characteristic polynomials of two induced operators (restricted and quotient space operators).

Published on 14 Apr 2026 - 11:01

score 135 · Answer 11 · 2026-03-25 06:08:54

135

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Invariant polynomial on matrices only involves diagonal elements?

Published on 25 Mar 2026 - 6:08

score 1.7k · Answer 12 · 2026-04-08 18:10:45

1.7k

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Finding the size of a matrix representing a linear transformation?

Published on 08 Apr 2026 - 18:10

score 1.4k · Answer 13 · 2026-04-15 22:32:35

1.4k

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The nonexistence of a Jordan normal form over a finite field

Published on 15 Apr 2026 - 22:32

score 79 · Answer 14 · 2026-04-13 19:16:32

79

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Using the property of determinant, verify that

Published on 13 Apr 2026 - 19:16

score 84 · Answer 15 · 2026-04-15 07:29:12

84

Views

If $n$ is odd and $a_{ij} = -a_{ji}$ for all $i,j\in\{1,...,n\}$, then $A$ is not invertible. Does the statement hold also when $n$ is even?

Published on 15 Apr 2026 - 7:29

List Question

Let $T, N :V \to V$, N is nilpotent, T is invertible and $NT = TN$. Prove $N+T$ invertible.

Solving least squares problem using partial derivatives

Here is my proof that the elementary $k$-forms form a basis for $A^k{(\mathbb{R}^n)}$. Is this correct?

Getting vectors and eigenvalue from an eigenvector problem

Prove that $T$ is a positive definite operator

Exercise on degree extensions of quadratic subfield over $\Bbb Q$

Find the vector in w in W closest to v.

Let T1 be the linear transformation corresponding to a counterclockwise rotation of 120 degrees

Merton 1972 efficiency frontier solution using linear algebra

Characteristic polynomial of operator is the product of characteristic polynomials of two induced operators (restricted and quotient space operators).

Invariant polynomial on matrices only involves diagonal elements?

Finding the size of a matrix representing a linear transformation?

The nonexistence of a Jordan normal form over a finite field

Using the property of determinant, verify that

If $n$ is odd and $a_{ij} = -a_{ji}$ for all $i,j\in\{1,...,n\}$, then $A$ is not invertible. Does the statement hold also when $n$ is even?

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