13 Oct 2014
Linear Algebra@Chapter 2
Tips before start:
is identity matrix with 2x2 size, i.e.
- matrix A is n x m, matrix B is a x b. AB has size n x b, m must equal a, since A is coefficient matrix, B is vector of variables, each variables get one coefficient (a column), so # of column in A = # of row in B.
- # of row in A is # of equation in the system, # of column in B is the # of column in the final matrix since each Ab will sum to one column
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Multiplication of Matrix
First at all, understand
Then, you can understand
can sum to one column,
is coefficient matrix,
is the vector of variables,
can sum to one column if the linear system is completed, i.e
. Different column in
means different linear system for
, so
will not sum with
.
only
Finally,
Power of Matrix
Transpose of matrix

Theorem
For d. please be reminded that
, b x a and
, m x n , gives out
with m x a
matrix A, n x m and matrix B, a x b, gives out AB with m x a,
therefore
u , v both in
,
and result in 1x1 matrix , called inner product
and result in n x n matrix, called outer product
Inverse of matrix
if
, if
, then A is singular, vice versa.
Determinants
