00:00 Intro

00:50 Algebraic and geometric multiplicities

01:33 Recipe

06:09 3x3 example

06:31 Step 1: eigenvalues

09:17 Step 2: eigenspaces

14:50 Step 3: eigenvectors

16:02 Credits

Q1: Consider the matrix $A \in \mathbb{C}^{n \times n}$. What is correct for the eigenspace $\mathrm{Eig}(\lambda)$.

A1: If $\lambda$ is an eigenvalue, the eigenspace is at least one-dimensional.

A2: $\mathrm{Eig}(\lambda)$ does not contain the zero vector.

A3: $\mathrm{Eig}(\lambda)$ is not a vector space.

A4: $\lambda \in \mathrm{Eig}(\lambda)$.

Q2: Consider the matrix $A \in \mathbb{C}^{n \times n}$. If $\lambda$ is an eigenvalue of $A$, how can you calculate the eigenspace $\mathrm{Eig}(\lambda)$?

A1: Do the Gaussion elimination for $(A - \lambda \mathbb{1})x = 0$.

A2: Do the Gaussion elimination for $(A + \lambda \mathbb{1})x = 0$.

A3: Do the Gaussion elimination for $A x = 0$.