Square matrix with complex entries that is equal to its own conjugate transpose.
[3 2+i; 2-i 1]
Positive Definite Matrix
A n x n real matrix M is positive definite if z’Mz > 0 for all non-zero vector z with real # entries.
z*Mz > 0 (for complex or Hermitian Matrix M)
[z_0 z_1] [1 0; 0 1] [z_0; z_1] = z_0^2 z_1^2
Therefore, [1 0; 0 1] is positive definite
Non-zero vectors that remain parallel to the original vector no matter what matrix (read: transformation) is applied to them.
Av = lamba *v, where lambda is the eigen value of A corresponding to v.
Decomposition of a Hermitian, positive-definite matrix into product of lower triangular matrix and its conjugate transpose (take the transpose then negate imaginary parts but not real part). Analogous to taking a square root of a number.
A = LL*, where L is a lower triangular matrix with positive diagonal entries.