Some “What’s the output” questions to get the day started…

>>A = [1 2 3; 3 5 6]

This statement stores the matrix:

1. A=1 2 3

3 5 6

2. A= 1 2 3 3 5 6

3. A=

1 3

2 5

3 6

4. A= Ask Garvin’s wife

What’s the output?

>>A = [1 2 3; 3 5 6]>>B = [2 4 6; 6 10 18]>>C = B./A

This statement stores the matrix:

1. C=2 2 2

2 2 3

2. C= 2 2 2 2 2 3

3. C=

2 2

2 2

2 3

4. Can’t divide these matrices

What’s the output?

>>A = [1 2 3; 3 5 6]>>B = [2 4 6; 6 10 18]>>C = B*A

This statement stores the matrix:

1. C=2 2 2

2 2 3

2. C= 2 2 2 2 2 3

3. C=

2 2

2 2

2 3

4. Can’t multiply these matrices: not the correct dimension – A is 2x3 B is 2x3

What’s the output?

>>A = [1 2 3; 3 5 6]>>B = [1 1 1; 1 1 1]>>C = B*A’

This statement stores the matrix:

1. C=6 14

6 14

2. C=

3. C=14 14

6 6

4. Can’t multiply these matrices: not the correct dimension – A is 2x3 B is 2x3

2 2 2

2 2 3

What’s the output?

>>A = [0:0.1:0.5]

This statement stores the matrix:

1. A= 0 0.1 0.2 0.3 0.4 0.5 2. A=

3. A= 4. A =

0

0 0.1 0.5 0.1 0.5

NEXT TOPIC: MATLAB FUNCTIONS

MATLAB uses function names consistent with most major programming languages

For example sqrt sin cos log

Function Input can be either scalars or matrices

Some functions return multiple results

size function determines the number of rows and columns

You can assign names to the output

There are functions for almost anything you want to do

Use the help feature to find out what they are and how to use them From the command window From the help selection on the menu

bar

Elementary Math Functions

abs(x) absolute valuesign(x) plus or minusexp(x) ex

log(x) natural loglog10(x) log base 10

Rounding Functions

round(x)fix(x)floor(x)ceil(x)

Trigonometric Functions

sin(x) sinecos(x) cosinetan(x) tangentasin(x) inverse sinesinh(x) hyperbolic sineasinh(x) inverse hyperbolic sinesind(x) sine with degree inputasind(x) inverse sin with degree output

Data Analysis

max(x)min(x)mean(x)median(x)sum(x)prod(x)sort(x)

When x is a matrix, the max is found for each column

max value

element number where the max value occurs

Returns both the smallest value in a vector x and its location in vector x.

Vector of maximums

Vector of row numbers

Returns a row vector containing the minimum element from each column of a matrix x, and returns a row vector of the location of the minimum in each column of matrix x.

Determining Matrix Sizesize(x) number of rows and columnslength(x) biggest dimension

Variance and Standard Deviation

std(x)var(x)

11

2

2

N

xN

kk

Random Numbers

rand(n) Returns an n by n matrix of

random numbers between 0 and 1

rand(n,m) Returns an n by m matrix of

random numbers

These random numbers are evenly distributed

Gaussian Random Numbers

randn(n) Returns an n by n matrix of

Gaussian (i.e. normal) random numbers with a mean of zero and a variance of 1.

randn(n,m) Returns an n by m matrix of

Gaussian (i.e. normal) random numbers with a mean of 0 and variance of 1

Manipulating Matrices

• Defining matrices• A matrix can be defined by typing in a list of numbers

enclosed in square brackets.• The numbers can be separated by spaces or

commas.• New rows are indicated with a semicolon.

A = [ 3.5 ];B = [1.5, 3.1]; or B =[1.5 3.1];C = [-1, 0, 0; 1, 1, 0; 0, 0, 2];

Manipulating Matrices

• Defining matrices• Define a matrix by using another matrix that has

already been defined.

• Reference an element in a matrix• Both row and column indices start from 1.

B = [1.5, 3.1]; S = [3.0, B]

S = [3.0, 1.5, 3.1]; T = [1 2 3; S]

S = 3.0 1.5 3.1 T = 1 2 3 3.0 1.5 3.1

S(2)

T(2, 2)

T(4)

The element value on row 2 and column 2 of matrix T

Count down column 1, then down column 2, and finally down column 2 to the correct element of matrix T.

Manipulating Matrices

• Change values in a matrix• S(2) = -1.0;

changes the 2nd value in the matrix S

from 1.5 to -1.0

• Extend a matrix by defining new elements.

S(4) = 5.5;Extend the matrix S to four elements instead of three.

S(8) = 9.5;Matrix S will have eight values, and the values of S(5), S(6), S(7) will be set to 0.

T(3, 3) = 10;T(4, 5) = 20;

Manipulating Matrices

• Using the colon operator• Define an evenly spaced matrix

H = 1:8 --- The default spacing is 1

time = 0.0:0.5:3.0 --- The middle value becomes the spacing.

• Extract data from matrices x = M( :, 1) --- extract column 1 from matrix M

y = M( :, 4) --- extract column 4 from matrix M

z = M(2, : ) --- extract row 2 from matrix M

a = M(2:3, : ) --- extract rows 2 and 3 from matrix M

b = M( :, 2:4) --- extract column 2 to column 4 from matrix M

c = M(2:3, 3:5) --- extract not whole rows or whole columns

from matrix M

• Converts a two dimensional matrix to a single column M( : )

M = 1 2 3 4 5 2 3 4 5 6 3 4 5 6 7