Unitary matrix

A complex matrix is unitary when

U^{†} U = U U^{†} = I

. Its columns form an orthonormal basis, and it preserves inner products and norms.

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Unitary matrix by

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A **unitary matrix** is a complex square matrix \( U \) that satisfies the condition: \[ U^\dagger U = U U^\dagger = I \] where \( U^\dagger \) is the conjugate transpose (also known as the Hermitian transpose) of \( U \), and \( I \) is the identity matrix of the same dimension as \( U \).

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Unitary matrix by

Ciro Santilli  40 Updated 2025-07-16

Complex analogue of orthogonal matrix.

Applications:

in quantum computers programming basically comes down to creating one big unitary matrix as explained at: quantum computing is just matrix multiplication

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