Main Diagonal

linear-algebra

Definition

Main Diagonal

The main diagonal of a matrix $M$ is the list of elements $M_{i,j}$ where $i=j$.

Example

Given a $3\times 3$ matrix $M$:

$$M=\left[\begin{array}{ccc}{M}_{1,1}& M_{1,2}& M_{1,3}\\ M_{2,1}& M_{2,2}& M_{3,3}\\ M_{3,1}& M_{3,2}& M_{3,3}\end{array}\right]$$

The main diagonal is:

$$\left\{M_{1,1},M_{2,2},M_{3,3}\right\}$$