Types of Matrices - SS3 Mathematics Lesson Note

COLUMN MATRIX: This is a matrix with one column of elements, example \(\begin{bmatrix} 3 \\ 1 \\ 7 \\ \end{bmatrix}\) has an order of \(3 \times 1\).

ZERO/NULL MATRIX: This matrix has all zeroes, example \(\begin{bmatrix} 0 & 0 \\ 0 & 0 \\ \end{bmatrix}\).

SQUARE MATRIX: A matrix that has equal number of rows and columns, example \(\begin{bmatrix} 1 & 4 & 0 \\ 5 & 3 & 8 \\ 4 & - 1 & 5 \\ \end{bmatrix}\) is a square matrix of order \(3 \times 3\). The elements \(1,\ 3\ and\ 5\) form the leading/main diagonal of the matrix. Note, only square matrices have a leading/main diagonal.

DIAGONAL MATRIX: A matrix whose entries are all zero except those along the leading diagonal, example \(\begin{bmatrix} 6 & 0 & 0 \\ 0 & - 5 & 0 \\ 0 & 0 & 11 \\ \end{bmatrix}\).

UNIT/IDENTITY MATRIX: A matrix whose entries in the leading diagonal are all unity (one), example \(\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}\).

EQUAL MATRICES: Two matrices are said to be equal if and only if they are both of same order and their corresponding values are equal. Given \(A = \begin{bmatrix} u & v \\ w & x \\ \end{bmatrix}\) and \(B = \begin{bmatrix} 2 & 5 \\ 0 & 9 \\ \end{bmatrix}\), as both \(A\) and \(B\) are of same order \(2 \times 2\) the \(A = B\) implies that \(u = 2,\ v = 5,\ w = 0\ and\ x = 9\).