Matrix Operations

1
Matrix Operations
2
Matrix Notation
3
Example
4
Equality of Matrices
5
Square Matrix
6
Diagonal Matrix
7
Triangular Matrices
8
Row and Column Vectors
9
Transposition of Vectors
10
Transposition of Matrices
11
Example
12
Symmetric and Skew-Symmetric Matrices
13
Addition of Matrices
14
Scalar Multiplication
15
Zero Matrix
16
Properties of Additon
17
Properties of Scalar Multiplication
18
Properties of Tranposition
19
Product of Matricies
20
Product of Matricies
21
Identity Matrices
22
Identity Property
23
A System of Linear Equations
24
The Matrix Equation Axb
25
Properties of Matrix Multiplication
26
Cautions
27
Matrix Powers
28
Theorem
29
Properties of Transposition
30
Definition of Linear Combination
31
Consistency Theorem for Linear Systems
A linear system Axb is consistent if and only if
b can be written as a linear combination of the
column vectors of A.
32
Definition
33
Matrix Inverse Identities