List questions from linear-algebra

Published on 24 Mar 2026 - 19:01

103

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Prove $T:V\rightarrow V$ is diagonalizable iff exists a basis $B$ of $V$ consisting unically of eigenvectors.

Published on 17 Feb 2018 - 23:07

84

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Prove about direct sum

Published on 17 Feb 2018 - 23:18

3.2k

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How to prove that $AB$ is invertible if and only if $A$ is invertible?

Published on 25 Mar 2026 - 3:21

33

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Prove $P_S(x)$ divide $P_T(x)$

Published on 18 Feb 2018 - 1:12

110

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Find a linear transformation with a specified kernel

Published on 27 Mar 2026 - 10:07

79

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Let $V=Mat_n(\mathbb{R})$ and $T:V\rightarrow V$ the linear operator $T(A)=A^t$. Find the characteristic polynomial of $T$

Published on 18 Feb 2018 - 4:01

1.3k

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What did Emil Artin mean when he said this?

Published on 25 Mar 2026 - 11:32

306

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Irreducibility of Symmetric N-Diagonal Matrix

Published on 26 Mar 2026 - 14:43

36

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Finding a point on a plane

Published on 18 Feb 2018 - 8:24

36

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Are these two transformations different? How?

Published on 27 Mar 2026 - 10:16

34

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Two ways for finding the basis and dim of the Image yield different results?

Published on 18 Feb 2018 - 9:44

567

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Find the values of the parameters for which the matrices commute

Published on 24 Mar 2026 - 23:45

67

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Transformation that rotates eigenvalues

Published on 24 Mar 2026 - 22:09

407

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Prove $tr(A)=\sum\limits_{\lambda\in Spec(A)} m_\lambda\lambda$

Published on 18 Feb 2018 - 12:19

List Question

Ordering rotational axis of symmetry

Prove $T:V\rightarrow V$ is diagonalizable iff exists a basis $B$ of $V$ consisting unically of eigenvectors.

Prove about direct sum

How to prove that $AB$ is invertible if and only if $A$ is invertible?

Prove $P_S(x)$ divide $P_T(x)$

Find a linear transformation with a specified kernel

Let $V=Mat_n(\mathbb{R})$ and $T:V\rightarrow V$ the linear operator $T(A)=A^t$. Find the characteristic polynomial of $T$

What did Emil Artin mean when he said this?

Irreducibility of Symmetric N-Diagonal Matrix

Finding a point on a plane

Are these two transformations different? How?

Two ways for finding the basis and dim of the Image yield different results?

Find the values of the parameters for which the matrices commute

Transformation that rotates eigenvalues

Prove $tr(A)=\sum\limits_{\lambda\in Spec(A)} m_\lambda\lambda$

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