The Eigen-Decomposition: Eigenvalues and Eigenvectors
3.2 Another definition for positive semi-definite ma-trices A matrix A is said to be positive semi-definite if we observe the following relationship for any non-zero vector x: xTAx ‚0 8x. (26) (when the relationship is • 0 we say that the matrix is negative semi-definite). When all the eigenvalues of a symmetric matrix are positive,
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