# Validate Operators¶

validate_operator is a module allowing one to check properties of operators or matrices.

 is_square_matrix(matrix) Checks if a matrix is square. is_symmetric_matrix(matrix, rtol, atol) Checks if a square matrix A is symmetric, $$A = A ^T$$, where $$^T$$ denotes transpose. is_identity_matrix(matrix, rtol, atol) Checks if a square matrix is the identity matrix. is_idempotent_matrix(matrix, rtol, atol) Checks if a square matrix A is idempotent, $$A^2 = A$$. is_normal_matrix(matrix, rtol, atol) Checks if a square matrix A is normal, $$A^\dagger A = A A^\dagger$$, where $$^\dagger$$ denotes conjugate transpose. is_hermitian_matrix(matrix, rtol, atol) Checks if a square matrix A is Hermitian, $$A = A^\dagger$$, where $$^\dagger$$ denotes conjugate transpose. is_unitary_matrix(matrix, rtol, atol) Checks if a square matrix A is unitary, $$A^\dagger A = A A^\dagger = Id$$, where $$^\dagger$$ denotes conjugate transpose and Id denotes the identity. is_positive_definite_matrix(matrix, rtol, atol) Checks if a square Hermitian matrix A is positive definite, $$eig(A) > 0$$. is_positive_semidefinite_matrix(matrix, …) Checks if a square Hermitian matrix A is positive semi-definite $$eig(A) \geq 0$$.