Question

Explain why the system of matrices $I, A, A^2, \ldots, A^{n^2 + 1}$ is dependent

score 101 · Answer 1 · 2023-10-29 23:49:11

101

Views

Explain why the system of matrices $I, A, A^2, \ldots, A^{n^2 + 1}$ is dependent

Published on 29 Oct 2023 - 23:49

score 16 · Answer 2 · 2026-02-23 10:20:10

16

Views

Prove each non-trivial solution, $u(x)$ of a normal, second-order linear ordinary differential equation, has only simple zeroes.

Published on 23 Feb 2026 - 10:20

score 34 · Answer 3 · 2023-11-16 19:12:26

34

Views

Dimension of space spanned by vectors subtracted by a linear combination of them

Published on 16 Nov 2023 - 19:12

score 66 · Answer 4 · 2023-11-21 17:40:42

66

Views

Is the method to prove that a code [n,k,d] punctured at $i$th index gives [n-1, k_i,d_i] code where $k_i\geq k-1$ is correct?

Published on 21 Nov 2023 - 17:40

score 173 · Answer 5 · 2023-11-23 12:31:04

173

Views

Let $f: [0,1]\to\mathbb{R}$ be injective. Does $\sum_{n=1}^{\infty} c_n\left( f(x)\right)^n=0\forall x\in [0,1] \implies c_n=0\forall n\in\mathbb{N}?$

Published on 23 Nov 2023 - 12:31

score 65 · Answer 6 · 2023-11-29 05:28:55

65

Views

How to find a linear combination of vectors that is congruent to $0\pmod 2$

Published on 29 Nov 2023 - 5:28

score 65 · Answer 7 · 2023-12-10 11:46:42

65

Views

Subtle conditions that imply linear independence

Published on 10 Dec 2023 - 11:46

score 26 · Answer 8 · 2023-12-23 22:34:08

26

Views

Linear independence as a way to gauge predictor usefulness.

Published on 23 Dec 2023 - 22:34

score 19 · Answer 9 · 2023-12-28 23:39:58

19

Views

Prove that $y_1(x) = y_{2}(x) \int_{}^{x} \frac{W(\tilde{x})}{y_1(x)^2\, d\tilde{x}$ for a non-vanishing Wronksian

Published on 28 Dec 2023 - 23:39

score 48 · Answer 10 · 2023-12-30 09:23:26

48

Views

If a basis for $V$ intersects an $m$-dimensional subspace of $V$ at $m$ basis vectors, will these $m$ vectors form a basis for the subspace?

Published on 30 Dec 2023 - 9:23

score 95 · Answer 11 · 2023-12-30 12:32:48

95

Views

If we have $n-1$ dependent vectors of size $n$, why if we remove the $i$th element from each, they're still dependent?

Published on 30 Dec 2023 - 12:32

score 17 · Answer 12 · 2024-01-03 17:01:59

17

Views

Independence of $\partial_t f(t,x)$ and $f(t,x)$ at a fixed time slice?

Published on 03 Jan 2024 - 17:01

score 67 · Answer 13 · 2024-01-13 19:08:19

67

Views

Is the set of vectors $(1, 0), (i, 0)$ a linearly independent subset of $\mathbb{C}^2(\mathbb{R})$?

Published on 13 Jan 2024 - 19:08

score 51 · Answer 14 · 2024-02-04 10:03:25

51

Views

I have confusion understanding why Zero Vector space has dimension zero?

Published on 04 Feb 2024 - 10:03

score 54 · Answer 15 · 2024-02-20 17:41:21

54

Views

Injectivity of linear combinations of linearly independent invertible operators

Published on 20 Feb 2024 - 17:41

List Question

Explain why the system of matrices $I, A, A^2, \ldots, A^{n^2 + 1}$ is dependent

Prove each non-trivial solution, $u(x)$ of a normal, second-order linear ordinary differential equation, has only simple zeroes.

Dimension of space spanned by vectors subtracted by a linear combination of them

Is the method to prove that a code [n,k,d] punctured at $i$th index gives [n-1, k_i,d_i] code where $k_i\geq k-1$ is correct?

Let $f: [0,1]\to\mathbb{R}$ be injective. Does $\sum_{n=1}^{\infty} c_n\left( f(x)\right)^n=0\forall x\in [0,1] \implies c_n=0\forall n\in\mathbb{N}?$

How to find a linear combination of vectors that is congruent to $0\pmod 2$

Subtle conditions that imply linear independence

Linear independence as a way to gauge predictor usefulness.

Prove that $y_1(x) = y_{2}(x) \int_{}^{x} \frac{W(\tilde{x})}{y_1(x)^2\, d\tilde{x}$ for a non-vanishing Wronksian

If a basis for $V$ intersects an $m$-dimensional subspace of $V$ at $m$ basis vectors, will these $m$ vectors form a basis for the subspace?

If we have $n-1$ dependent vectors of size $n$, why if we remove the $i$th element from each, they're still dependent?

Independence of $\partial_t f(t,x)$ and $f(t,x)$ at a fixed time slice?

Is the set of vectors $(1, 0), (i, 0)$ a linearly independent subset of $\mathbb{C}^2(\mathbb{R})$?

I have confusion understanding why Zero Vector space has dimension zero?

Injectivity of linear combinations of linearly independent invertible operators

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