Assertion: transpose | /r/HasProperty | equal
Facets:
value: to its inverse
type: OTHER
value: exactly
type: DEGREE
value: to negative
type: OTHER
value: with every entry
type: OTHER
value: to the matrix
type: OTHER
value: to itself
type: TRANSITIVE-OBJECT
Source sentences:
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 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 matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, A is orthogonal 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: The Transpose of an addition of two matrices A and B obtained will be exactly equal to the sum of the transpose of individual matrix A and B.
text: The Transpose of the product of two matrices is equal to the product of the transpose of the two matrices in reverse order.
text: Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse:
text: Equivalently, a matrix A is orthogonal if its transpose is equal to its inverse: