Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

Home Math Background Matrices Fundamental Theorems for Matrices
See also: matrix algebra 

Fundamental Theorems for Matrices

The following collection of formulas contains the most important rules of matrix algebra:

A + B = B + A

(A + B) + C = A + (B + C)

(AB)C = A(BC)

C(A + B) = CA + CB

λ(A + B) = λA + λB

Transposed matrices:

(AT)T = A

(A + B)T = AT + BT

(AB)T = BTAT

  (ABC)T = CTBTAT

Inversion of matrices:

 (AB)-1 = B-1A-1

   (ABC)-1 = C-1B-1A-1

(A-1)-1 = A

(AT)-1 = (A-1)T
Home Math Background Matrices Fundamental Theorems for Matrices