11 - Square Matrix

Square Matrix

Equal number of rows and columns ($m=n$)

Types of Square Matrices ( $A=(a_{ij})$)

1. Symmetric

$$A^T=A$$

2. Skew-Symmetric (or antisymmetric)

$$A^T=-A$$

Entries along the main diagonal are 0
3) Upper Triangular

$$a_{ij}=0⟺i>j$$

Entries below the diagonal are zero
4) Strictly Upper Triangular

$$a_{ij}=0⟺i\ge j$$

Entries on or below the main diagonal are zero
5) Triangular

$$\text{Either upper or lower triangular}$$