unitary matrix
Conjugate transpose inverts it
A unitary matrix is a square matrix whose conjugate transpose equals its inverse.
Unitary matrices preserve vector lengths and angles under multiplication, making them fundamental in quantum mechanics and signal processing.
They are the complex-number generalization of orthogonal matrices: The quantum gate is represented by a unitary matrix.
Distance-preserving map
- orthonormalPerpendicular and unit-length
- determinantMatrix-derived scalar quantity
- eigenvaluesTransformation scaling constants
- spectralGhostlike or wavelength-related
adjoint · invertible · inverse · transpose
Direction preserved under transformation
- eigenvalueScalar satisfying determinant equation
- diagonalizationReducing to diagonal form
- operatorOne who works machinery
- complex numbersNumbers containing imaginary components
Physics at nanoscopic scales
- wavefunctionQuantum state's mathematical representation
- Schrodinger equationQuantum state evolution law
- observablesQuantities that can be detected
- quantum statesProbabilistic particle descriptions
qubit · superposition · entanglement · measurement · quantum computing
isometry
Distance-preserving map
- orthonormalPerpendicular and unit-length
- determinantMatrix-derived scalar quantity
- eigenvaluesTransformation scaling constants
spectral · adjoint · invertible · inverse · transpose
eigenvector
Direction preserved under transformation
- eigenvalueScalar satisfying determinant equation
- diagonalizationReducing to diagonal form
- operatorOne who works machinery
quantum mechanics
Physics at nanoscopic scales
- wavefunctionQuantum state's mathematical representation
- Schrodinger equationQuantum state evolution law
- observablesQuantities that can be detected
quantum states · qubit · superposition · entanglement · measurement · quantum computing
- linear algebralinear equation, vectors, linear function, determinant, variables
- matricestranspose, determinants, rows, cells
- Unitary Groups
- operator theoryoperator, adjoint, spectrum, eigenvalue, eigenvector
- eigenvalueseigenvalue, eigenvector, eigenvalues, eigenvectors, eigendecomposition
- vector spacesvector, basis, dimension, subspace, eigenvector