# Questions tagged [positive-semidefinite]

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

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### Checking positive semidefiniteness in MATLAB

Let $\mathbf{A}$ be a $n\times n$ matrix. I want to check in MATLAB if it is PSD or not. Which tests, in MATLAB, should I do for this purpose? I know that if $\mathbf{A}$ is PSD then following holds ...
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### Can this matrix be negative definite?

Let $d = 12$ and $m = 6$, and denote by $0_n$ and $I_n$ the zero matrix and the identity matrix of size $n \times n$. Let $D_+ \in \mathbb{R}^{m \times m}$ be a diagonal matrix with positive ...
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### Semidefinite Matrix in LINGO

Using LINGO, I need to enter the following block matrix as one of my constraints $M= \left[ {\begin{array}{cc} 1 & x^T \\ x & X \\ \end{array} } \right]$ where x is an n by 1 ...
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### Eigenvalues and positive semidefiniteness of a special matrix

Consider the following $(n+1)\times(n+1)$ real matrix $$A=\begin{pmatrix}a&p^t\\p&D\end{pmatrix},$$ where $D$ is an $n\times n$ diagonal matrix with strictly positive entries, $a>0$, and ...