Properties of matrix addition - Matrices

Properties of matrix addition

Lessons

Notes:
Let the matrices X,YX,Y and ZZ have equal dimensions. Then we have the following matrix addition properties:

Dimension property for addition
If XX and YY has the same dimensions, then X+YX+Y also has the same dimensions.
Commutative property
X+Y=Y+XX+Y=Y+X
Associative property
(X+Y)+Z=X+(Y+Z)(X+Y)+Z=X+(Y+Z)

There are also some matrix addition properties with the identity and zero matrix.

Property for the zero matrix
There is always a zero matrix OO such that O+X=XO+X=X for any matrix XX.
Property for the identity matrix
Let XX be a nn by nn matrix. Then there is an identity matrix InI_n such that InX=XI_n \cdot X=X.
  • 2.
    Verifying the matrix addition properties
    You are given that and and . Verify the following properties:
  • 3.
    You are given that and and . Verify the following properties:
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Properties of matrix addition

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