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Title: Sylvester’s Criterion
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Series: Multivariable Calculus
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Chapter: Extrema of Functions
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YouTube-Title: Multivariable Calculus 20 | Sylvester’s Criterion
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: mc20_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Timestamps
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
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Subtitle in English (n/a)
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Quiz Content
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: $$ \begin{pmatrix} 2 & 1 \ 0 & 1 \end{pmatrix} $$
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Last update: 2024-10
