List questions from positive-definite

Published on 20 Sep 2016 - 13:06

207

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On one property of positive semidefinite matrices

Published on 26 Mar 2026 - 11:31

478

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Is there a relation between trace of congruent matrices?

Published on 21 Sep 2016 - 11:55

1.2k

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Showing that positive definite symmetric matrices have a smooth square root

Published on 22 Sep 2016 - 10:55

48

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For a positive definite matrix $Q$ and any square matrices $A_i$, if $\sum_{i=1}^pA_i^TQA<Q$, can we get $\rho(\sum_{i=1}^pA_i^TA)<1$?

Published on 24 Sep 2016 - 2:06

63

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Let $W$ be a square matrix. If $W+W'$ is positive definite, what one can say about $W$?

Published on 25 Sep 2016 - 0:47

931

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On positive definite matrices, hermitian, positive eigenvalues and square roots

Published on 01 Oct 2016 - 6:11

22.7k

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Do positive semidefinite matrices have to be symmetric?

Published on 27 Mar 2026 - 2:34

1.5k

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Why positive definite matrix implies minimum?

Published on 09 Oct 2016 - 12:37

26k

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Why do positive definite matrices have to be symmetric?

Published on 11 Oct 2016 - 16:53

1.1k

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$y^TX^TXy$ achieves minimum when its second derivative is positive definite.

Published on 12 Oct 2016 - 21:01

70

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Show that a matrix $A$ is positive definite if and only if $ A + A^T$ is positive definite

Published on 13 Oct 2016 - 4:00

42

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Show that a matrix $A$ is positive definite in $\mathbb{C^2}$ under some conditions

Published on 13 Oct 2016 - 19:03

67

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Definiteness of a matrix

Published on 15 Oct 2016 - 11:39

40

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linear algebra - challenging proof (property of definite real matrix)

Published on 16 Oct 2016 - 11:16

List Question

Is the matrix square root uniformly continuous?

On one property of positive semidefinite matrices

Is there a relation between trace of congruent matrices?

Showing that positive definite symmetric matrices have a smooth square root

For a positive definite matrix $Q$ and any square matrices $A_i$, if $\sum_{i=1}^pA_i^TQA<Q$, can we get $\rho(\sum_{i=1}^pA_i^TA)<1$?

Let $W$ be a square matrix. If $W+W'$ is positive definite, what one can say about $W$?

On positive definite matrices, hermitian, positive eigenvalues and square roots

Do positive semidefinite matrices have to be symmetric?

Why positive definite matrix implies minimum?

Why do positive definite matrices have to be symmetric?

$y^TX^TXy$ achieves minimum when its second derivative is positive definite.

Show that a matrix $A$ is positive definite if and only if $ A + A^T$ is positive definite

Show that a matrix $A$ is positive definite in $\mathbb{C^2}$ under some conditions

Definiteness of a matrix

linear algebra - challenging proof (property of definite real matrix)

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