Square Matrix

linear-algebra

Definition

Square Matrix

Let $M=(a_{ij})$ be a matrix. $M$ is square if it has the same number of rows and columns.

Eigenvalue

If $A\in F^{n\times n}$ is a square matrix, then $\lambda$ is an eigenvalue of $A$ if there exists $v\ne 0$ such that

$$Av=\lambda v$$

This holds if and only if $\lambda$ is a root of the characteristic polynomial:

$$\det (\lambda I-A)=0$$