Assertion: matrix's transpose | /r/HasProperty | equal
Facets:
value: to its inverse
type: OTHER
value: to negative
type: OTHER
value: to itself
type: TRANSITIVE-OBJECT
value: to it
type: OTHER
value: with every entry
type: OTHER
value: to the matrix
type: OTHER
Source sentences:
text: 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
text: 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
text: A square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, A is unitary if
text: Hence, the only case where the transpose of a matrix can be equal to it is when the matrix is square.
text: Whenever this happens for any matrix, that is whenever transpose of a matrix is equal to it, the matrix is known as a symmetric matrix.
text: So, if for a matrix A,\(a_{ij}\) = \(a_{ji}\) (for all the values of i and j) and m = n , then its transpose is equal to itself.
text: If the transpose of a matrix is equal to the negative of itself, the matrix is said to be skew symmetric.
text: Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse:
text: A square matrix whose transpose is equal to itself is called a symmetric matrix; that is, A is symmetric if
text: A square matrix whose transpose is equal to its negative is called a skew-symmetric matrix; that is, A is skew-symmetric if
text: A square matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, A is orthogonal if
text: Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse: