A matrix whose eigenvalues are all positive or zero valued is called positive semidefi-
nite.

University of Michigan - Ann Arbor

Suppose that a matrix A has n linearly independent eigenvectors {$v^{(1)}$, . . . , $v^{(n)}$} with corresponding eigenvalues {$\lambda _1$, . . . , $\lambda _n$}. We may concatenate all the eigenvectors to form a matrix V with one eigenvector per column: V = [$v^{(1)}$ , . . . , $v^{(n)}$]. Similarly, we can get a vector containing eigenvalues, naming it as $\lambda$. The eigendecomposition of A is then given by
$A = Vdiag(\lambda)V^{-1}$

Linear Algebra - eigendecomposition

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

Deep Learning

A matrix is singular if and only if any of the eigenvalues are zero.

Singular Matrix Judgement According to Eigenvalues

A matrix whose eigenvalues are all positive is called positive definite.

Positive Definite

Positive Semidefinite

If all eigenvalues are negative, the matrix is negative definite.

Negative Definite

If all eigenvalues are negative or zero valued, it is negative semidefinite.

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