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Exercise 11.8.4

Avg difficulty 3.0

Use Descartes’ rule of signs to determine which of the following matrices are positive definite and/or positive semidefinite.

A=[2221],B=[2−10−110001],C=[21−111100−102−110−11].A=\left[\begin{array}{cc}2&2\\ 2&1\\ \end{array}\right],\quad B=\left[\begin{array}{ccc}2&-1&0\\ -1&1&0\\ 0&0&1\\ \end{array}\right],\quad C=\left[\begin{array}{cccc}2&1&-1&1\\ 1&1&0&0\\ -1&0&2&-1\\ 1&0&-1&1\\ \end{array}\right].

Selinger, Matrix Theory and Linear Algebra, Inner product spaces, Positive semidefinite and positive definite matrices, Exercise 11.8.4

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.