Matrix Shorthand

To express Matrix Operations more concisely, we can use a shorthand notation where it is expressed generally in terms of $i,j$ where:

• $i$ represents the row index
• $j$ represents the column index

Example

Consider a matrix $\mathbf{A}$ with $m$ rows and $n$ columns:

$$\mathbf{A}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]={\left[\begin{array}{c}{a}_{ij}\end{array}\right]}_{m\times n}$$

And if I want to transpose the matrix we can write using shorthand:

$${\mathbf{A}}^T={\left[\begin{array}{c}{a}_{ji}\end{array}\right]}_{n\times m}$$