Question

Show that the matrix $AA^T+\alpha I$ is positive definite, where $\alpha >0$ and $A$ is an $m\times n$ real matrix.

score 192 · Answer 1 · 2016-04-26 14:42:41

192

Views

Show that the matrix $AA^T+\alpha I$ is positive definite, where $\alpha >0$ and $A$ is an $m\times n$ real matrix.

Published on 26 Apr 2016 - 14:42

score 2.5k · Answer 2 · 2016-05-01 16:34:13

2.5k

Views

Does $AB+BA=0$ imply $AB=BA=0$ when $A$ is real semidefinite matrix?

Published on 01 May 2016 - 16:34

score 153 · Answer 3 · 2016-05-02 03:13:43

153

Views

Prove that the inner product $\langle f,g\rangle= \int f(t)g(t) \, dt $ satisfies the property positive definiteness

Published on 02 May 2016 - 3:13

score 324 · Answer 4 · 2016-05-04 02:16:24

324

Views

Prove positive definite of a function

Published on 04 May 2016 - 2:16

score 399 · Answer 5 · 2016-05-05 07:43:18

399

Views

When can we say a symmetric matrix is positive semi definite matrix?

Published on 05 May 2016 - 7:43

score 96 · Answer 6 · 2016-05-09 03:46:30

96

Views

tell Positive Definite Matrices by the sign of determinants

Published on 09 May 2016 - 3:46

score 35 · Answer 7 · 2016-05-09 23:47:25

35

Views

Integral of $f(x)$ of region between $y=0$ and $y=4-x^2$

Published on 09 May 2016 - 23:47

score 106 · Answer 8 · 2016-05-10 21:05:33

106

Views

What is the condition for n by n symmetric matrix with 1 on diagonal and x everywhere else to be positive definite

Published on 10 May 2016 - 21:05

score 86 · Answer 9 · 2026-03-27 07:50:50

86

Views

Positive definitiveness of a product of matrices

Published on 27 Mar 2026 - 7:50

score 1k · Answer 10 · 2016-05-12 10:11:00

1k

Views

Almost negative definite matrices and norm-distance matrices

Published on 12 May 2016 - 10:11

score 262 · Answer 11 · 2016-05-13 03:52:34

262

Views

Show that $det \left( {A+B} \right) \geq det\left( {A} \right)$

Published on 13 May 2016 - 3:52

score 460 · Answer 12 · 2026-03-27 07:37:20

460

Views

Why am I not getting two positive pivots for this symmetric matrix?

Published on 27 Mar 2026 - 7:37

score 709 · Answer 13 · 2016-05-18 07:56:06

709

Views

Can $A^{T}(AA^{T})^{-1}A$ be simplified?

Published on 18 May 2016 - 7:56

score 114 · Answer 14 · 2016-05-18 11:44:14

114

Views

Product of the differences of two pd matrices and their respective inverses is pd

Published on 18 May 2016 - 11:44

score 91 · Answer 15 · 2016-05-20 13:14:42

91

Views

Evaluate the product $\operatorname{tr}(AB)\operatorname{tr}(CB^{-1})$

Published on 20 May 2016 - 13:14

List Question

Show that the matrix $AA^T+\alpha I$ is positive definite, where $\alpha >0$ and $A$ is an $m\times n$ real matrix.

Does $AB+BA=0$ imply $AB=BA=0$ when $A$ is real semidefinite matrix?

Prove that the inner product $\langle f,g\rangle= \int f(t)g(t) \, dt $ satisfies the property positive definiteness

Prove positive definite of a function

When can we say a symmetric matrix is positive semi definite matrix?

tell Positive Definite Matrices by the sign of determinants

Integral of $f(x)$ of region between $y=0$ and $y=4-x^2$

What is the condition for n by n symmetric matrix with 1 on diagonal and x everywhere else to be positive definite

Positive definitiveness of a product of matrices

Almost negative definite matrices and norm-distance matrices

Show that $det \left( {A+B} \right) \geq det\left( {A} \right)$

Why am I not getting two positive pivots for this symmetric matrix?

Can $A^{T}(AA^{T})^{-1}A$ be simplified?

Product of the differences of two pd matrices and their respective inverses is pd

Evaluate the product $\operatorname{tr}(AB)\operatorname{tr}(CB^{-1})$

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