-
Title: Sylvester’s Criterion
-
Series: Multivariable Calculus
-
Chapter: Extrema of Functions
-
YouTube-Title: Multivariable Calculus 20 | Sylvester’s Criterion
-
Bright video: https://youtu.be/KeAQi5aZSIg
-
Dark video: https://youtu.be/NTH4CDlZuTI
-
Ad-free video: Watch Vimeo video
-
Forum: Ask a question in Mattermost
-
Quiz: Test your knowledge
-
Dark-PDF: Download PDF version of the dark video
-
Print-PDF: Download printable PDF version
-
Thumbnail (bright): Download PNG
-
Thumbnail (dark): Download PNG
-
Subtitle on GitHub: mc20_sub_eng.srt missing
-
Download bright video: Link on Vimeo
-
Download dark video: Link on Vimeo
-
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
-
Subtitle in English (n/a)
-
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: $$ \begin{pmatrix} 2 & 1 \ 0 & 1 \end{pmatrix} $$
-
Last update: 2024-10
