advanced-linear-algebra

Positive definite and semidefinite matrices

taught

The full definiteness classification -- positive/negative (semi)definite, indefinite -- read directly off a symmetric matrix's eigenvalue signs, generalizing chapter 04's signature to the language this chapter uses throughout.

Taught in

Positive definite and semidefinite matrices
Advanced Linear Algebra

Requires

ellipsoids-and-the-shape-of-a-positive-definite-matrix required
signature-and-classification-of-quadratic-forms required

Required by

Four tests for definiteness, and when each is the right one required
The Rayleigh quotient required

Local knowledge map

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.