Question

Prove $k(AB) \leq k(A)k(B)$ where $k(\cdot)$ denotes the condition number

score 3.1k · Answer 1 · 2011-11-02 05:23:01

3.1k

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Prove $k(AB) \leq k(A)k(B)$ where $k(\cdot)$ denotes the condition number

Published on 02 Nov 2011 - 5:23

score 5.6k · Answer 2 · 2012-08-26 13:37:36

5.6k

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Matrices whose condition number is $1$

Published on 26 Aug 2012 - 13:37

score 898 · Answer 3 · 2012-10-30 06:19:41

898

Views

Condition number of $2 \times 2$ block matrix in terms of the singular values of the off-diagonal blocks

Published on 30 Oct 2012 - 6:19

score 161 · Answer 4 · 2026-03-25 16:39:58

161

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Condition number of $A^{-1} B$ where $A$ and $B$ are banded Toeplitz matrices.

Published on 25 Mar 2026 - 16:39

score 997 · Answer 5 · 2026-03-25 16:44:21

997

Views

If $\kappa (A) > \kappa (B)$, show $\kappa (B^{-1}A) < \kappa (A)$

Published on 25 Mar 2026 - 16:44

score 150 · Answer 6 · 2020-08-12 07:33:31

150

Views

Condition number for the relative residual of the matrix square root

Published on 12 Aug 2020 - 7:33

score 446 · Answer 7 · 2020-08-12 14:57:17

446

Views

Wilkinson's polynomial very simple misunderstanding

Published on 12 Aug 2020 - 14:57

score 211 · Answer 8 · 2020-08-16 15:58:33

211

Views

Show that: if $Cond_2(A)=1$ then $A=\alpha Q$; where $Q $ is an orthonormal matrix and $\alpha$ is a real number $\neq 0$

Published on 16 Aug 2020 - 15:58

score 859 · Answer 9 · 2020-08-21 09:49:42

859

Views

Norm-wise condition number vs component-wise condition number

Published on 21 Aug 2020 - 9:49

score 75 · Answer 10 · 2020-08-22 07:40:55

75

Views

How to Prove that $ cond(A)\ge \frac{||A||}{||C||} $ for any induced matrix norm. With $A$ invertible and $A+C$ singular matrix

Published on 22 Aug 2020 - 7:40

score 132 · Answer 11 · 2020-09-11 13:58:35

132

Views

How does lattice reduction algorithm reduce condition number of a matrix?

Published on 11 Sep 2020 - 13:58

score 46 · Answer 12 · 2020-09-21 00:29:17

46

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$\left[\operatorname{cond}(A)\right]^2 = \|{A}\|^2\|\left(A^TA\right)^{-1}\|$ for $m \times n$ matrix $A, m > n.$

Published on 21 Sep 2020 - 0:29

score 60 · Answer 13 · 2020-10-07 19:44:19

60

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what does condition number of not complete power of 10 imply?

Published on 07 Oct 2020 - 19:44

score 2.2k · Answer 14 · 2026-03-25 16:01:11

2.2k

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Condition number of a positive definite matrix

Published on 25 Mar 2026 - 16:01

score 78 · Answer 15 · 2020-10-17 15:33:54

78

Views

Find the Condition Number for $w\left(a+b\right)=a^2+b^2$

Published on 17 Oct 2020 - 15:33

List Question

Prove $k(AB) \leq k(A)k(B)$ where $k(\cdot)$ denotes the condition number

Matrices whose condition number is $1$

Condition number of $2 \times 2$ block matrix in terms of the singular values of the off-diagonal blocks

Condition number of $A^{-1} B$ where $A$ and $B$ are banded Toeplitz matrices.

If $\kappa (A) > \kappa (B)$, show $\kappa (B^{-1}A) < \kappa (A)$

Condition number for the relative residual of the matrix square root

Wilkinson's polynomial very simple misunderstanding

Show that: if $Cond_2(A)=1$ then $A=\alpha Q$; where $Q $ is an orthonormal matrix and $\alpha$ is a real number $\neq 0$

Norm-wise condition number vs component-wise condition number

How to Prove that $ cond(A)\ge \frac{||A||}{||C||} $ for any induced matrix norm. With $A$ invertible and $A+C$ singular matrix

How does lattice reduction algorithm reduce condition number of a matrix?

$\left[\operatorname{cond}(A)\right]^2 = \|{A}\|^2\|\left(A^TA\right)^{-1}\|$ for $m \times n$ matrix $A, m > n.$

what does condition number of not complete power of 10 imply?

Condition number of a positive definite matrix

Find the Condition Number for $w\left(a+b\right)=a^2+b^2$

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