NLA MT25, Gaussian random matrices
Flashcards
@Define a Gaussian random matrix.
A matrix $G \in \mathbb R^{m \times n}$ where $G _ {ij} \sim N(0, 1)$.
@State what is meant by the orthogonal invariance of Gaussian random matrices $G$.
The distribution of an orthogonal random matrix is invariant under orthogonal matrix, i.e. if:
- $G$ is a Gaussian matrix
- $Q$ is an orthogonal matrix independent of $G$
Then:
- $QG$ and $GQ$ are both Gaussian random matrices