00:00 Intro

00:54 Assumptions of Sylvester’s Criterion

02:07 Sylvester’s Criterion for positive definite matrices

03:57 Sylvester’s Criterion for negative definite matrices

04:45 Proof for diagonal matrices

06:34 Example calculation

08:57 Credits

Q1: For which matrix is Silvester’s criterion applicable?

A1: $$ \begin{pmatrix} 2 & 1 \ 1 & 1 \end{pmatrix} $$

A2: $$ \begin{pmatrix} 2 & 1 \ 2 & 1 \end{pmatrix} $$

A3: $$ \begin{pmatrix} 2 & 1 \ -2 & 1 \end{pmatrix} $$

A4: $$ \begin{pmatrix} 2 & 1 \ 0 & 1 \end{pmatrix} $$

Q2: Which of the following matrices is positive definite?

A1: $$ \begin{pmatrix} 2 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 4 \end{pmatrix} $$

A2: $$ \begin{pmatrix} 2 & 0 & 0 \ 0 & -6 & 0 \ 0 & 0 & 4 \end{pmatrix} $$

A3: $$ \begin{pmatrix} 2 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 4 \end{pmatrix} $$

A4: $$ \begin{pmatrix} 2 & 1 \ 0 & 1 \end{pmatrix} $$