Hermitian matrices
Equal their conjugate transpose
A Hermitian matrix is a square matrix that equals its own conjugate transpose—meaning when you flip it across its diagonal and take the complex conjugate of each entry, you get the same matrix back.
These matrices are fundamental in quantum mechanics and linear algebra because they always have real eigenvalues and orthogonal eigenvectors.
The observable quantities in quantum physics are represented by Hermitian matrices.
Named after the French mathematician Charles Hermite.
definiteness
Matrix ensuring positivity
- indefiniteNot precisely determined
- convexityOutward-curving quality
structure
Minute remnant or pursue
- determinantMatrix-derived scalar quantity
- bandedHaving encircling marks
- sparseThinly scattered or distributed
spectral
Transformation scaling constants
- eigenvectorsVectors scaled by matrices
- diagonalizationReducing to diagonal form
- multiplicityState of being many
positive definite
Matrix ensuring positivity
- indefiniteNot precisely determined
- convexityOutward-curving quality
trace
Minute remnant or pursue
- determinantMatrix-derived scalar quantity
- bandedHaving encircling marks
- sparseThinly scattered or distributed
observable
Capable of being detected
- quantum mechanicsPhysics at nanoscopic scales
eigenvalues
Transformation scaling constants
- eigenvectorsVectors scaled by matrices
- diagonalizationReducing to diagonal form
- multiplicityState of being many
eigendecomposition
Factoring via eigenvectors
- matricestranspose, determinants, rows, cells
- eigenvalueseigenvalue, eigenvector, eigenvalues, eigenvectors, eigendecomposition