transpose conjugate
English
Noun
transpose conjugate (plural transpose conjugates)
- (mathematics) The transpose of a matrix, after replacing each element with its complex conjugate.
- 2006, David Andrews, Lumped Element Quadrature Hybrids[1], page 22:
- Further constraints upon the four-port are discovered when the elements equating to zero in the product of the unitary S-matrix with its transpose conjugate are considered.
- 2012, Steven B. Damelin, Willard Miller, Jr., The Mathematics of Signal Processing, page 299,
- In that case the inverse of the matrix is just the transpose conjugate and solving for the original signal x from the truncated outputs {y(0)(2n)},{y(1)(2n)} is simple.
- 2012, Dennis M. Sullivan, Quantum Mechanics for Electrical Engineers[2], page 85:
- Throughout this text, the transpose conjugate of a matrix or vector is given by A+ or b+, respectively.
Usage notes
In linear algebra, it may be denoted using the notations A*, AH, A† or A+. Of these, the superscripted dagger (glyph) notation is universally used in quantum mechanics. Also, the notation A+ is commonly used for the Moore–Penrose pseudoinverse.
In some contexts, A* denotes the matrix of complex conjugate entries, and the transpose conjugate is then denoted by A*T or AT*.
Synonyms
- (transpose of matrix of complex conjugates): adjoint matrix, bedaggered matrix, conjugate transpose, Hermitian conjugate, Hermitian transpose, transjugate
See also
- adjugate matrix (historically also sometimes called "adjoint")