Notesale: Turn your study into money

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MATRICES
TYPES OF MATRICES:
1) Zero matrix

2) Square matrix
Mmxn , the number of rows m is equal to the number of columns n

3) Identity matrix
Is a square matrix + it has Maa=1 and Mbb=0

4) Diagonal matrix
Is a square matrix + Mab=0
Example:

5) Upper triangular matrix
Is a square matrix + Mab=0 below the diagonal

6) Lower triangular matrix
Is a square matrix + Mab=0 above the diagonal

7) Symmetric matrix
Is a square matrix and Mab=Mba

8) Antisymmetric matrix
Is a square matrix + Mab=-Mba and Maa=0

MATRIX ADDITION :
Note: you can NOT add two matrices unless they have the
same dimensions
Example:

Some of its propreties:
1
...
it is commutative ,ex: A+B=B+A
3
...
upper triangular + upper triangular = upper triangular
(we add their diagonal coefficients)
5
...
antisymmetric + antisymmetric = antisymmetric

MATRIX TRANSPOSE :
When transposing a matrix , the row becomes column and the
column becomes row

Some of it propreties:

if it is a diagonal matrix
if it is an identity matrix
if it is a symmetric matrix
if it an antisymmetric matrix

MATRIX MULTIPLICATION:
Note: you can not multiply two matrices unless the
number of columns of the first matrix is equal as the
number of rows of the second one ex: Mmxn * Mnxf

da
some of its propreties :
1
...
BC= A
...
C
3
...
B
...
B
...
A
...
A
...

6
...
I A
7
...
0 0 and 0
...
diagonal * diagonal = diagonal ( you multiply their diagonal coefficients)
9
...
A*B=0 si A=0 or B=0 we also call something nilpotent when
A*A*A*A*…=0 (when thw product of itself multiple times will be equal to
zero)

MATRIX INVERSION:



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