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**Maths for Computer Graphics 2011-2012**

Matrices Maths for Computer Graphics

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**Matrix Matrix an array of numbers arranged into m rows and n columns:**

i = 1, …, m Columns, j = 1, …, n

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**Row and Column Matrices (vectors)**

row matrix (or row vector) is a matrix with one row column vector is a matrix with only one column

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Square Matrix When the row and column dimensions of a matrix are equal (m = n) then the matrix is called square matrix

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Matrix Equality Two (m x n) matrices A and B are equal if and only if each of their elements are equal. That is A = B if and only if aij = bij for all i = 1,...,m; j = 1,...,n

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Matrix Addition 2x2 Matrix addition

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Matrix Addition

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**Examples - Matrix Addition**

The following matrix addition is not defined

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**Scalar – Matrix Multiplication**

Multiplication of a matrix A by a scalar is defined as follows Example

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**Matrix – Matrix Multiplication**

The product of two matrices A and B is defined only if the number of columns of A is equal to the number of rows of B. If A is (m x p) and B is (p x n), the product is an (m x n) matrix C

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**Matrix – Matrix Multiplication**

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**Matrix – Matrix Multiplication**

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**Example - Matrix Multiplication**

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**Example - Matrix Multiplication**

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**Example - Matrix Multiplication**

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**Identity Matrix Identity Matrix**

The identity matrix has the property that if A is a square matrix, then

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