Whats so great about matrices with orthonormal columnsSoluti

What\'s so great about matrices with orthonormal columns?

Solution

matrix with orthonormal columns are defined such that A^TA = I (identity matrix)

Orthogonal matrix: a   square   real matrix with orthonormal column.

Further , square matrices with orthonormal columns also have orthonormal rows.

They are known as Orthogonal matrix: The columns of A form an orthonormal basis.

Geometric meaning: An orthogonal matrix preserves its length and angle

If A is an orthogonal matrix then det(A) =1.

An orthogonal matrix with determinant +1 is a rotation.

Orthogonal matrices with determinant -1 are generally are not rotations and most of them are neither reflections

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