What is the "matrix-norm" of a vector?

Question

What does this notation mean?

$$ ||\mathbf{x}||_{A} $$

• $\mathbf{x} \in \mathbb{R}^n$
• $A \in \mathbb{R}^{n \times n}$ a square matrix (positive definite, if that happens to be relevant).

Searches for "matrix norm" always refer to norms for matrices.

Answer 1

It can mean $\sqrt{\mathbf{x}^T A \mathbf{x}}$, you can look into "The Mahalanobis Norm" or "The Energy Norm" for more details/googling.

Edit: as mentioned in a comment below, it more commonly refers to $\|x\|_A :=\sqrt{\mathbf{x}^T A^{-1} \mathbf{x}}$, which is frequently used in statistics.