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A square matrix with complex entries is called unitary if
The following theorem parallels Theorem 6.6.1.
THEOREM 10.6.2
Equivalent Statements
If is an matrix with complex entries, then the following are equivalent.
(a) is unitary.
(b) The row vectors of form an orthonormal set in with the Euclidean inner product.
(c) The column vectors of form an orthonormal set in with the Euclidean inner product.
EXAMPLE 2 A Unitary Matrix
The matrix
(1)
has row vectors
Relative to the Euclidean inner product on , we have
and
so the row vectors form an orthonormal set in . Thus is unitary and
