• Title: Sylvester’s Criterion

• Series: Multivariable Calculus

• YouTube-Title: Multivariable Calculus 20 | Sylvester’s Criterion

• Bright video: https://youtu.be/KeAQi5aZSIg

• Dark video: https://youtu.be/NTH4CDlZuTI

• Subtitle on GitHub: mc20_sub_eng.srt missing

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

• Back to overview page