Question

Is the null space (line) of any linear transformation $T:\Bbb R^3\to\Bbb R^3$ perpendicular to the range (plane)?

score 291 · Answer 1 · 2018-03-02 16:48:37

Is the null space (line) of any linear transformation $T:\Bbb R^3\to\Bbb R^3$ perpendicular to the range (plane)?

score 137 · Answer 2 · 2026-03-25 06:34:57

137

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Is the the $n \times n$ matrix $A_{ij} = (ij + 1)^m$, $m \geq n$ invertible?

Published on 25 Mar 2026 - 6:34

score 63 · Answer 3 · 2026-04-03 14:06:23

63

Views

Need to do an opposite operation to a dot product with non square matrices, cannot figure out how.

Published on 03 Apr 2026 - 14:06

score 64 · Answer 4 · 2026-03-22 20:00:59

64

Views

if $||AB||_\infty<1$ is I-AB is positive definite ? provided A,B are symmetric and A+B is positive definite

Published on 22 Mar 2026 - 20:00

score 141 · Answer 5 · 2018-03-02 18:18:35

141

Views

The diagonal entries of a Hermitian tend to infinity, all entries of its inverse are zero

Published on 02 Mar 2018 - 18:18

score 609 · Answer 6 · 2026-03-23 06:32:00

609

Views

Spectrum of an infinite matrix

Published on 23 Mar 2026 - 6:32

score 243 · Answer 7 · 2026-03-27 04:39:36

243

Views

Volume of a paralellepiped

Published on 27 Mar 2026 - 4:39

score 145 · Answer 8 · 2018-03-02 19:32:48

Let $A, B \in \mathbb{M}_3(\mathbb{C})$ such that $\det(A) = \det(B) = 1.$ Show that $\det(A + \sqrt{2}\cdot B) \not= 0.$

score 607 · Answer 9 · 2026-03-27 12:02:00

607

Views

$T$ has no eigenvalues

Published on 27 Mar 2026 - 12:02

score 643 · Answer 10 · 2026-03-25 06:00:18

643

Views

Finding the Intersection Value of a Linear Equation and a Power Function with a Negative Exponent

Published on 25 Mar 2026 - 6:00

score 228 · Answer 11 · 2026-03-25 01:29:08

228

Views

Extending the Proof for $\det(AB) = \det(A) \cdot \det(B)$ from the $3 \times 3$ to the $n \times n$ case

Published on 25 Mar 2026 - 1:29

score 63 · Answer 12 · 2026-03-25 04:42:57

63

Views

Why $b_0$ and $b_1$ from linear regression $(y = b_0 + b_1\cdot x)$ are calculated like follows? How is the formula for such variables derived?

Published on 25 Mar 2026 - 4:42

score 298 · Answer 13 · 2026-03-26 18:50:32

298

Views

How to make the eigenvalue of this matrix inside or on the unit circle?

Published on 26 Mar 2026 - 18:50

score 49 · Answer 14 · 2026-03-26 09:26:17

49

Views

Structure of linear maps between vector spaces of same dimension.

Published on 26 Mar 2026 - 9:26

score 80 · Answer 15 · 2026-03-24 23:46:23

80

Views

Rotation of state-transition matrix to a chosen parametric form

Published on 24 Mar 2026 - 23:46

List Question

Is the null space (line) of any linear transformation $T:\Bbb R^3\to\Bbb R^3$ perpendicular to the range (plane)?

Is the the $n \times n$ matrix $A_{ij} = (ij + 1)^m$, $m \geq n$ invertible?

Need to do an opposite operation to a dot product with non square matrices, cannot figure out how.

if $||AB||_\infty<1$ is I-AB is positive definite ? provided A,B are symmetric and A+B is positive definite

The diagonal entries of a Hermitian tend to infinity, all entries of its inverse are zero

Spectrum of an infinite matrix

Volume of a paralellepiped

Let $A, B \in \mathbb{M}_3(\mathbb{C})$ such that $\det(A) = \det(B) = 1.$ Show that $\det(A + \sqrt{2}\cdot B) \not= 0.$

$T$ has no eigenvalues

Finding the Intersection Value of a Linear Equation and a Power Function with a Negative Exponent

Extending the Proof for $\det(AB) = \det(A) \cdot \det(B)$ from the $3 \times 3$ to the $n \times n$ case

Why $b_0$ and $b_1$ from linear regression $(y = b_0 + b_1\cdot x)$ are calculated like follows? How is the formula for such variables derived?

How to make the eigenvalue of this matrix inside or on the unit circle?

Structure of linear maps between vector spaces of same dimension.

Rotation of state-transition matrix to a chosen parametric form

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