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Sahithyan's S1

Introduction to Matrices

Revise Matrices unit from G.C.E. (A/L) Combined Mathematics and G.C.E. (O/L) Mathematics.

Types of matrices

Square matrix

Number of columns equal to number of rows.

Diagonal matrix

A square matrix whose only non-zero elements are main-diagonal elements. Denoted by . Subset of triangular matrices.

Identity matrix or Unit matrix

A diagonal matrix whose diagonal elements are all equal to . Denoted by . Subset of diagonal matrices.

Zero matrix / Null matrix

All elements are .

Column matrix (column vector)

Only column.

Row matrix (row vector)

Only row.

Triangular matrix

Upper triangular matrix or lower triangular matrix.

Upper triangular matrix

All elements below the main diagonal are . Subset of square matrices.

Lower triangular matrix

All elements above the main diagonal are . Subset of square matrices.

Matrix operations

Addition and subtraction

Order of the 2 matrices must be same. Matrix obtained by adding or subtracting corresponding elements.

Scalar multiplication

Matrix obtained by multiplying all elements by the scalar.

Matrix multiplication

Explained on a separate page: Matrix multiplication