List of matrices

Columns: Name | Explanation | Notes
Circular matrix or Coninvolutory matrix | A matrix whose inverse is equal to its entrywise complex conjugate : A = A | Compare with unitary matrices | Congruent matrix | Two matrices A and B are congruent if there exists an invertible matrix P such that P A P = B | Compare with similar matrices | EP matrix or Range-Hermitian matrix | A square matrix that commutes with its Moore-Penrose inverse : AA = A A | Idempotent matrix or Projection Matrix | A matrix that has the property A ² = AA = A | The name projection matrix inspires from the observation of projection of a point multiple times onto a subspace ( plane or a line ) giving the same result as one projection | Invertible matrix | A square matrix having a multiplicative inverse , that is , a matrix B such that AB = BA = I | Invertible matrices form the general linear group | Involutory matrix | A square matrix which is its own inverse , i.e. , AA = I | Signature matrices , Householder Matrices ( Also known as 'reflection matrices ' to reflect a point about a plane or line ) have this property | Nilpotent matrix | A square matrix satisfying A = 0 for some positive integer q | Equivalently , the only eigenvalue of A is 0 | Normal matrix | A square matrix that commutes with its conjugate transpose : AA = A A | They are the matrices to which the spectral theorem applies

Example questions:
What is the explanation for a satisfying conditions on products or inverses complex square matrix A is normal if it commutes with its conjugate transpose A* ? | What is the explanation for a satisfying conditions on products or inverses matrix that is its own inverse ?

Answers:
spectral theorem | I