Matrix Theorems
Here, we list without proof some of the most important rules of matrix algebra -
theorems that govern the way that matrices are added, multiplied,
and otherwise manipulated.
Notation
Matrix Addition and Matrix Multiplication
-
A + B =
B + A
(Commutative law of addition)
-
A + B + C =
A + ( B + C ) =
( A + B ) + C
(Associative law of addition)
-
ABC =
A( BC ) =
( AB )C
(Associative law of multiplication)
-
A( B + C ) =
AB
+ AC
(Distributive law of matrix algebra)
-
x( A + B ) =
xA
+ xB
Transposition Rules
-
( A' )' = A
-
( A + B )' =
A' + B'
-
( AB )' =
B'A'
-
( ABC )' =
C'B'A'