List questions from linear-transformations

Published on 26 Mar 2026 - 10:46

54

Views

Is it the same $a^\alpha + b^\alpha = x$ as $(a^\alpha)^\frac{1}{\alpha} + (b^\alpha)^\frac{1}{\alpha} = x^\frac{1}{\alpha}$

Published on 25 Mar 2026 - 19:25

250

Views

Proof Expla.: $\lambda$ is an eigenvalue of $A\in M_{n\times n}(F)$ iff $\det(A-\lambda I)=0$?

Published on 18 Jul 2018 - 16:39

210

Views

RCF of $(x^2+1)^2$

Published on 19 Jul 2018 - 1:15

8.9k

Views

Is dot product a kind of linear transformation

Published on 19 Jul 2018 - 2:39

327

Views

self-adjoint linear map has determinant $ < 0$.

Published on 26 Mar 2026 - 1:09

512

Views

If $V,W$ are finite-dimensional and $T: V \to W$ , $S: W \to V$ are injective linear maps then $T$ is an isomorphism

Published on 26 Mar 2026 - 10:43

54

Views

Extract a vector that is in the middle of a matrix equation

Published on 27 Mar 2026 - 1:46

138

Views

Multilinear transformations being determined by their values on basis elements

Published on 25 Mar 2026 - 12:52

77

Views

High Schooler (Advanced Linear Algebra Help)

Published on 26 Mar 2026 - 3:19

45

Views

Linear transformations with restricted range

Published on 24 Mar 2026 - 22:09

827

Views

calculating the location of a point relative to another origin

Published on 25 Mar 2026 - 17:40

1.4k

Views

$T$ is injective if and only if $ST=I_V$ for some $S\in\mathcal{L}(W,V)$.

Published on 25 Mar 2026 - 1:38

213

Views

Linear Transformations between 2 non-standard basis of Polynomials

Published on 21 Jul 2018 - 15:41

278

Views

How to find dimensions of skew-symmetric diagonal matrices.

Published on 22 Jul 2018 - 1:30

List Question

Attempt to proof following statement (kernel and image of a matrix)

Is it the same $a^\alpha + b^\alpha = x$ as $(a^\alpha)^\frac{1}{\alpha} + (b^\alpha)^\frac{1}{\alpha} = x^\frac{1}{\alpha}$

Proof Expla.: $\lambda$ is an eigenvalue of $A\in M_{n\times n}(F)$ iff $\det(A-\lambda I)=0$?

RCF of $(x^2+1)^2$

Is dot product a kind of linear transformation

self-adjoint linear map has determinant $ < 0$.

If $V,W$ are finite-dimensional and $T: V \to W$ , $S: W \to V$ are injective linear maps then $T$ is an isomorphism

Extract a vector that is in the middle of a matrix equation

Multilinear transformations being determined by their values on basis elements

High Schooler (Advanced Linear Algebra Help)

Linear transformations with restricted range

calculating the location of a point relative to another origin

$T$ is injective if and only if $ST=I_V$ for some $S\in\mathcal{L}(W,V)$.

Linear Transformations between 2 non-standard basis of Polynomials

How to find dimensions of skew-symmetric diagonal matrices.

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