Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [positive-semidefinite]

Relating to a symmetric $n\times n $ real matrix $(M)$ such that the scalar $x^TMx\ge 0\ \forall x\in \Bbb{R}^n\backslash {0}$

If $M$ is a positive semidefinite matrix then it has some additional properties which can be found in this Wikipedia article. You can also use this tag if one or more of these properties leads back to $M$ being positive-semidefinite.

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This matrix is positive semi-definite. Why?

This example in Stephen Boyd's Convex Optimization book says that the following matrix is element-wise positive and therefore $x^TQx$ is semi-definite where $Q=W - \lambda_{min}(W)(I) \succcurlyeq 0$. The example appears in Sec. 5.1.5, just before…
sprajagopal
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Sum of positive semi-difinite matrix inequality

Can the following conclusion hold? There exist matrices $H^i\in\mathbb{R}^{m\times n}, (m\leq n, i\in\mathcal{N})$, and non-zero real numbers $\underline{h}^i$, and $\overline{h}^i$. If the following inequality holds…
wayne
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How to prove that the determinant of a matrix must be very small (close to 0)?

In equation $\mathbf{b=Aa}$, if all the entries in $\mathbf{A}$ and $\mathbf{b}$ are bounded, and $||\mathbf{a}|| \to \infty$. Then how to prove that det$(\mathbf{A})$ $\to 0$ (be very close to 0 but not equal to 0)? $||\mathbf{a}|| \to \infty$…
Xiankun Xu
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Positive Semi-Definite Matrix products

If A and C are positive definite and symmetric matrices and B is a positive semi-definite matrix and symmetric. Would the Product (assuming the dimensions match) i.e T=ABC be positive semi-definite? A sort of sub question in this same line of though…
user1421195
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How can I get the following equation w.r.t. positive semidefinite symmetric matrix?

There are matrices; $x_k$, $u_k$, $A_k$, $B_k$, and $Q_k$ whose dimension are $[n\times1]$, $[m\times1]$, $[n\times n]$, $[n\times m]$, and $[n\times n]$, respectively, such that $$x_{k+1}=A_kx_k+B_ku_k+w_k.$$ Another condition is that the matrices…
Danny_Kim
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$S^TAS$ is positive semidefinite

I need to prove this: If A is an n$\times$n positive semidefinite matrix, and S any $n \times m$ matrix, then $S^TAS$ is positive semidefinite.
what_456
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