Matrix’s determinant
Signing:
singular
Theorem: 
, 
Proof: without proof.
Definition:
A and B matrix’s are similar if 
T regular : 
Theorem: the similarity is an equivalent relation.
Proof: it comes from the theorem.
Theorem: every square matrix is similar with a triangle one.
Proof: without proof.
Determinant determination:
n=2 :
=
n=3:
=
We can count it like it because of the permutation.
Theorem:
1.
2.
3.The determinants of similar matrix’s are the same.
Proof:
1. 
2. 
, 
3. 
Q.E.D.
Determinant of a triangle matrix: the product of the elements in the main counter-diagonal.
La Place endorsement
Definition:
A matrix, then
matrix is created from ‘A’ by leaving its “i” row and “j” column.
Theorem: 
Proof:
without proof.
column
endorsement after the j-th column.
For example:
j=2
For example:
j=1
Adjungated matrix
Definition:
i,j adjungated unit.
Definition:
A adjungated matrix.
For example:
Theorem: A is a regular one (quadratic matrix), then
Proof:
(theorem)
a, 
La Place endorsement after the 
column.
b, 
is the same as the determinant of the matrix, created by the changing of the 
row to the 
row.
and 
row are the same
the matrix is a singular one
, 
3. 
/multiplication from left 
/
Q.E.D
For example:
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