the transpose of a matrix equals the inverse when it flips a matrix over its diagonal.
the transpose of a matrix equals the inverse when it flips a matrix over its diagonal.
when does the transpose of a matrix equal the inverse?
flips a matrix over its diagonal
a square complex matrix whose transpose is equal to the negation of its complex conjugate is called a skew-hermitian matrix; that is, a is skew-hermitian if









































a square matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, a is orthogonal if









































a square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, a is unitary if









































section::::products.
transpose
section::::special transpose matrices.









































a square matrix whose transpose is equal to itself is called a symmetric matrix; that is, a is symmetric if









































a square matrix whose transpose is equal to its negative is called a skew-symmetric matrix; that is, a is skew-symmetric if









































a square complex matrix whose transpose is equal to the matrix with every entry replaced by its complex conjugate (denoted here with an overline) is called a hermitian matrix (equivalent to the matrix being equal to its conjugate transpose); that is, a is hermitian if
transpose