Download Presentation
Matrix Algebra Basics

Loading in 2 Seconds...

1 / 30

# Matrix Algebra Basics - PowerPoint PPT Presentation

Matrix Algebra Basics. Pam Perlich Urban Planning 5/6020. Algebra. Matrix. A matrix is any doubly subscripted array of elements arranged in rows and columns. Row Vector. [1 x n] matrix. Column Vector. [m x 1] matrix. Square Matrix. Same number of rows and columns. The Identity.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Matrix Algebra Basics' - Sophia

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Matrix Algebra Basics

Pam Perlich

Urban Planning 5/6020

Matrix

A matrix is any doubly subscripted array of elements arranged in rows and columns.

Row Vector

[1 x n] matrix

Column Vector

[m x 1] matrix

Square Matrix

Same number of rows and columns

Identity Matrix

Square matrix with ones on the diagonal and zeros elsewhere.

Transpose Matrix

Rows become columns and columns become rows

Matrix Addition and Subtraction

A new matrix C may be defined as the additive combination of matrices A and B where: C = A + B

is defined by:

Note: all three matrices are of the same dimension

Addition

If

and

then

Matrix Subtraction

C = A - B

Is defined by

Matrix Multiplication

Matrices A and B have these dimensions:

[r x c] and [s x d]

Matrix Multiplication

Matrices A and B can be multiplied if:

[r x c] and [s x d]

c = s

Matrix Multiplication

The resulting matrix will have the dimensions:

[r x c] and [s x d]

r x d

Computation: A x B = C

[2 x 2]

[2 x 3]

[2 x 3]

Computation: A x B = C

[3 x 2]

[2 x 3]

A and B can be multiplied

[3 x 3]

Computation: A x B = C

[3 x 2]

[2 x 3]

Result is 3 x 3

[3 x 3]

Matrix Inversion

Like a reciprocal in scalar math

Like the number one in scalar math

Linear System of Simultaneous Equations

First precinct: 6 arrests last week equally divided between felonies and misdemeanors.

Second precinct: 9 arrests - there were twice as many felonies as the first precinct.

Note: Inverse of

is

Solution

Premultiply both sides by inverse matrix

A square matrix multiplied by its inverse results in the identity matrix.

A 2x2 identity matrix multiplied by the 2x1 matrix results in the original 2x1 matrix.

General Form

n equations in n variables:

unknown values of x can be found using the inverse of matrix A such that

Garin-Lowry Model

The object is to find x given A and y . This is done by solving for x :

Matrix Operations in Excel

Select the cells in which the answer will appear

Matrix Multiplication in Excel
• Enter “=mmult(“
• Select the cells of the first matrix
• Enter comma “,”
• Select the cells of the second matrix
• Enter “)”
Matrix Multiplication in Excel

Enter these three key strokes at the same time:

control

shift

enter

Matrix Inversion in Excel
• Follow the same procedure
• Select cells in which answer is to be displayed
• Enter the formula: =minverse(
• Select the cells containing the matrix to be inverted
• Close parenthesis – type “)”
• Press three keys: Control, shift, enter