Orthogonal Matrix Explained With Examples

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Before we study the Orthogonal Matrix, let us understand the definition of the Transpose of a matrix and Identity matrix.

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‘Transpose’ of a matrix (say A) is a matrix obtained by interchanging its rows into columns or columns into rows. It can be denoted as A Transpose.

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‘Identity Matrix’ is a square matrix that has 1s on the main diagonal and zeros everywhere else. A 3×3 identity matrix can be written as

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If the product of a matrix and its transpose results in an identity matrix, we call that matrix an ‘Orthogonal Matrix’.

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Let us see the example that explains whether or not the given matrix is an Orthogonal matrix.

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Consider a matrix

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Now find the production A and A transpose and see what is the result.

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