Question

For any full rank matrix, $A \in \mathbb{R}^{n \times n}$, show that $A + A^T$ is symmetric (but not necessarily positive definite) and $AA^T$ is both symmetric and positive-definite.

Name: For any full rank matrix, A ∈ℝ^n × n, show that A + A^T is symmetric (but not necessarily positive definite) and AA^T is both symmetric and positive-definite.
Uploaded: 2022-02-18T03:01:07-08:00
Duration: 1 min 44 s
Channel: Nick Johnson
Description: For any full rank matrix, A ∈ℝ^n × n, show that A + A^T is symmetric (but not necessarily positive definite) and AA^T is both symmetric and positive-definite.

          For any full rank matrix, $A \in \mathbb{R}^{n \times n}$, show that $A + A^T$ is symmetric (but not necessarily positive definite) and $AA^T$ is both symmetric and positive-definite.