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Introduction to Matrices

- ME-190
- Jan. 2004
- Dr. W. Farrow

Square Matrix

- Order 3 x 3 (since m n it can be written 3)
- Matlab definition
- A a11 a12 a13 a21 a22 a23 a31 a32 a33

Column Matrix (Column Vector)

- Order 3 x 1
- Matlab definition
- A a11 a21 a31

Row Matrix (Row Vector)

- Order 1 x 3
- Matlab definition
- A a11 a12 a13

General Matrix Form

- Order m x n (m - of rows, n - of

columns) - Matlab definition
- A a11 a12 a1n a21 a22 a2n a31 a32 a3n

- am1 am2 amn

Zero Matrix

- Order m x n (m - of rows, n - of

columns) - Matlab definition
- A zeros(m, n)

Square Zero Matrix

- Order n ( for this example 3)
- Matlab definition
- A zeros(n)

Ones Matrix

- Order m x n (m - of rows, n - of

columns) - Matlab definition
- A ones(m, n)

Random Number Matrix

- Fills the matrix with random numbers 0 lt a lt 1
- Order m x n (m - of rows, n - of

columns) - Matlab definition
- A rand(m, n)

Identity Matrix

- Order n ( for this example 3)
- Matlab definition
- A eye(n)

System of Linear Equations

- A matrix can be used to represent a system of

Linear equations - a11 x1 a12 x2 a13x3 b1
- a21 x1 a22 x2 a23x3 b2
- a31 x1 a32 x2 a33x3 b3
- A X B

Matrix Representation ofa System of Linear

Equations

- AX B

Array Operationsvs Matrix Operations

- Addition Subtraction
- Same for both Arrays and Matrices
- Add corresponding elements
- Both must have same order

Array Operationsvs Matrix Operations

- Addition Subtraction
- MatLab syntax
- C A B or C A - B

Array Operationsvs Matrix Operations

- Multiplication of Arrays .
- Different than for Matrices
- Multiply corresponding elements
- Both must have same order or one must be scalar

Array Operationsvs Matrix Operations

- Multiplication of Matrices (linear algebraic

operation) - Multiply elements of rows in matrix on left, with

corresponding elements of column in matrix on

right, sum the results and place in new matrix - The matrices must be conformable or one must be

scalar

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