MATLAB

Lecture TwoTuesday 5 July 2005

Chapter 3

Matrices and Vectors

Input matrix• A = [ 1 2 5; 3 9 0]

Use semicolon ";" to suppress output

Use … for line continuation

Matrices and Vectors

Vector is a special case of matrix Scalar is considered 1x1 matrix

• g = 9.81 (no [ … ] needed) X = [ ] creates a null matrix

Examples on page 51.

Matrices and Vectors

Matrix indexing• A(i,j) ith row jth column• A(m:n, k:l) specifies submatrix• A(:, j) jth column• A(i,:) ith row• A(m:k:n,:) row m, m+k,m+2k, etc.

Matrices and Vectors

Dimension• B(2,3) = 5• matrix B created large enough to

have the (2,3) entry, I.e., B is 2 x 3. The dimension is increased

dynamically

Matrices and Vectors

Matrix Manipulation• array as index, A([1 3 4],:)

reshape(…) function Transpose by .’ Hermitian conjugate by ’ Initialization

Matrices and Vectors

Appending a row or column• A = [A; u]; A = [ A u']

Deleting a row or column• A(2, :) = [ ], delete 2nd row• A(:,1) = [ ], delete 1st column

Matrices and Vectors

Utility matrices• eye(m,n), zeros(m,n), ones(m,n),

rand(m,n), diag(A)

rot90, fliplr, flipud, tril, triu

Examples on page 56

Matrices and Vectors

Creating vectors• v= initialV : increment : finalV

• e.g., a = 0:10:100

linspace(a,b,n) and logspace(a,b,b) functions

Matrices and Vectors

Matrix operations• + addition• - subtraction• * multiplication• / division• ^ exponentiation

Matrices and Vectors

Left division and right division• A / B is A B-1 (right division)

• A \ B is A-1 B (left division), in particular the solution to equation Ax = b, is x = A\b.

Matrices and Vectors

Element-by-element operation• .* element-wise multiply• ./ element-wise right division• .\ element-wise left division • .^ element-wise exponentiation• .' nonconjugated transpose

Examples on page 60.

Relational Operations

< Less than <= Less than or equal == equal > greater than >= greater than or equal ~= not equal (different from C)

Logical Operations

& logical AND | logical OR ~ logical complement (NOT) xor exclusive OR (a function)

Logical Functions

all, any, exist, isempty, isinf, isfinite, isnan, find

Math Functions

sin, asin, cos, acos, tan, atan, atan2, sec, cot, sinh, exp, log, log10, sqrt, abs, angle, conj, real, imag, fix, floor, ceiling, sign, etc.

Matrix functions• expm(A), logm(A), sqrtm(A)

Character Strings

Strings are quoted by single quotes• message = 'Leave me alone'

Strings are considered as 1xn matrix.

Eval Function

Eval interprets string as a MATLAB commend• eval('x = 5*sin(pi/3)')

Lookfor

Lookfor search for key word in the function documentation

eigenvalue example

Save and Loading Data

save • save entire workspace in the file

matlab.mat load

• load the saved file save file.mat x y z

• save the values x, y, z in file.mat

Recording a Session with "diary"

diary filename• Save the session to filename

diary off• Turn of the diary recording

Plotting

plot(x, y)

plot(x1,y1,x2,y2)

xlabel, ylabel, title, print

Exercises

Lesson 5, exercise 3.• Write a function factorial to computer

factorial n! for any integer n.

Exercises

Lesson 5, exercise 5.• Write a function to compute the sum

of a geometric series 1 + r + r2 + r3 + … + rn for a given r and n.

Exercises on page 74, problem 1, 4, and 5

Enter matrices• A = [2 6; 3 9]• B = [1 2; 3 4]• C = [-5 5; 5 3]

Create a big matrix that has A, B, C on the diagonal

Exercises on page 74, problem 1, 4, and 5

Delete the last row and last column

Extract the first 4x4 matrix from G Replace G(5,5) with 4 What do you get for G(13)? What happens if you type G(12,1)