Question

Inverse of a triangular-by-block $3 \times 3$ matrix

score 140 · Answer 1 · 2026-03-17 15:06:51

140

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Inverse of a triangular-by-block $3 \times 3$ matrix

Published on 17 Mar 2026 - 15:06

score 424 · Answer 2 · 2026-03-20 04:58:29

424

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Proving whether a matrix is invertible

Published on 20 Mar 2026 - 4:58

score 76 · Answer 3 · 2026-03-22 07:00:10

76

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Proof verification : Assume $A$ is a $n×m$ matrix, and $B$ is $m×n$. Prove that $AB$, an $n×n$ matrix is not invertible, if $n>m$.

Published on 22 Mar 2026 - 7:00

score 502 · Answer 4 · 2026-03-21 10:54:19

502

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Help with proof or counterexample: $A^3=0 \implies I_n+A$ is invertible

Published on 21 Mar 2026 - 10:54

score 50 · Answer 5 · 2026-03-20 00:35:39

50

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Show that if $a_1,\ldots,a_n$ are elements of a group then $(a_1\cdots a_n)^{-1} =a_n^{-1} \cdots a_1^{-1}$

Published on 20 Mar 2026 - 0:35

score 53 · Answer 6 · 2026-03-20 10:54:54

53

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Simplifying $\tan^{-1} {\cot(\frac{-1}4)}$

Published on 20 Mar 2026 - 10:54

score 177 · Answer 7 · 2026-03-20 05:05:59

177

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Invertible matrix and inverse matrix

Published on 20 Mar 2026 - 5:05

score 75 · Answer 8 · 2026-03-22 12:35:28

75

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show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$

Published on 22 Mar 2026 - 12:35

score 96 · Answer 9 · 2026-03-22 08:28:56

96

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Inverse matrix for $M_{kn}=\frac{i^{(k-n)}}{2^n}\sum_{j=0}^{n} (-1)^j \binom{n}{j}(n-2j)^k$

Published on 22 Mar 2026 - 8:28

score 2.5k · Answer 10 · 2026-03-19 19:36:31

2.5k

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What is the determinant modulo 2?

Published on 19 Mar 2026 - 19:36

score 644 · Answer 11 · 2026-03-20 09:04:47

644

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If A is such that $(A+2I)^2=0$, prove that $A+I$ is invertible.

Published on 20 Mar 2026 - 9:04

score 2.2k · Answer 12 · 2026-03-20 06:56:16

2.2k

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Prove that the set of invertible elements in a Banach algebra is open

Published on 20 Mar 2026 - 6:56

score 387 · Answer 13 · 2026-03-20 03:46:03

387

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Are most linear operators invertible?

Published on 20 Mar 2026 - 3:46

score 164 · Answer 14 · 2026-03-20 03:17:57

164

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A good estimation of the inverse $f^{-1}(x)$ of $-\sum_{n=2}^\infty\frac{\mu(n)}{n}x^n$, over the unit inverval if it has mathematical meaning

Published on 20 Mar 2026 - 3:17

score 53 · Answer 15 · 2026-03-20 09:05:42

53

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Determination of Invertibility

Published on 20 Mar 2026 - 9:05

List Question

Inverse of a triangular-by-block $3 \times 3$ matrix

Proving whether a matrix is invertible

Proof verification : Assume $A$ is a $n×m$ matrix, and $B$ is $m×n$. Prove that $AB$, an $n×n$ matrix is not invertible, if $n>m$.

Help with proof or counterexample: $A^3=0 \implies I_n+A$ is invertible

Show that if $a_1,\ldots,a_n$ are elements of a group then $(a_1\cdots a_n)^{-1} =a_n^{-1} \cdots a_1^{-1}$

Simplifying $\tan^{-1} {\cot(\frac{-1}4)}$

Invertible matrix and inverse matrix

show $f(x)=f^{-1}(x)=x-\ln(e^x-1)$

Inverse matrix for $M_{kn}=\frac{i^{(k-n)}}{2^n}\sum_{j=0}^{n} (-1)^j \binom{n}{j}(n-2j)^k$

What is the determinant modulo 2?

If A is such that $(A+2I)^2=0$, prove that $A+I$ is invertible.

Prove that the set of invertible elements in a Banach algebra is open

Are most linear operators invertible?

A good estimation of the inverse $f^{-1}(x)$ of $-\sum_{n=2}^\infty\frac{\mu(n)}{n}x^n$, over the unit inverval if it has mathematical meaning

Determination of Invertibility

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