Matrices, definitions

Summary

• A matrix \(A\) is a rectangular array of numbers.
• An \(n×m\) matrix \(A\) is a matrix with \(n\) rows and \(m\) columns (the dimension of the matrix).
• If \(A\) is a matrix then \(a_{i,j}\) denotes the individual item in row \(i\) and column \(j\) (called an element of the matrix \(A\) ).
• Two matrices \(A,B\) are said to be equal if they have the same dimension and all the elements are equal.
• General notation for an \(n×m\) matrix \(A\) :

\[A=\begin{bmatrix} a_{1,1} & \cdots & a_{1,m} \\ a_{2,1} & \cdots & a_{2,m} \\ \vdots & \ddots & \vdots \\ a_{n,1} & \cdots & a_{n,m} \end{bmatrix}\]