The document outlines the use of MATLAB for creating and manipulating matrices, including syntax for defining row and column vectors, accessing elements, and performing mathematical operations. It covers built-in functions, logical operations, and how to extract portions of matrices, as well as provides examples of matrix manipulations. Additionally, it discusses various powerful matrix functions available in MATLAB for advanced operations.

2. 1. >> for = 5
??? for = 5
Error: The expression to the left of the equals sign is not a valid target
for an assignment
2. >> else =6
??? else = 6
Error: Illegal use of reserved keyword "else"
3. >> cos = 2; cos(0)
??? Subscript indices must either be real positive integers or logicals
4. >> A = [1,2,3]; sum(A)
ans = 6
>> sum = 7; sum(A)
??? Index exceeds matrix dimensions
2

3. 5. >> 5>2
ans = 1
6. >> 5<4
ans = 0
7. >> 1.5<=1.5
ans = 1
8. >> 2>=pi
ans = 0
9. >> 1.8==1.801
ans = 0
10. >> 1.8~=2
ans = 1
11. >> 1.8==1.80000000000000000000000001
ans = 1
3

4.  Creating and manipulating matrices
 Built-in functions for matrices
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5.  Matlab treats all variables as matrices.
 Vectors are special forms of matrices and contain only one row OR
one column (A row vector is a 1xn matrix, A column vector is an mx1
matrix).
 Scalars are matrices with only one row AND one column (A scalar is a
1x1 matrix)
 Every matrix element has a numerical value. Non-digit elements
linked to ASCII code digits
A → 65, B → 66, etc.
a → 97, b → 98, etc.
- → 45, _ → 95, etc.
 Logical truth values assigned to digits (true → 1, false → 0)
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6.  A matrix with only one row is called a row
vector.
 A row vector can be created in Matlab as
follows (note the commas or you can use
spaces):
» rowvec = [12 , 14 , 63]
rowvec =
12 14 63
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7.  A matrix with only one column is called a
column vector.
 A column vector can be created in MATLAB as
follows (note the semicolons):
» colvec = [13 ; 45 ; -2]
colvec =
13
45
-2
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8.  A matrix can be created in Matlab as follows
 (note the commas AND semicolons):
 » matrix = [1 , 2 , 3 ; 4 , 5 ,6 ; 7 , 8 , 9]
matrix =
1 2 3
4 5 6
7 8 9
8

9.  A portion of a matrix can be extracted and stored in
a smaller matrix by specifying the names of both
matrices and the rows and columns to extract.
 The syntax is:
sub_matrix = matrix ( r1 : r2 , c1 : c2 ) ;
where r1 and r2 specify the beginning and ending
rows and c1 and c2 specify the beginning and
ending columns to be extracted to make the new
matrix.
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10. 10

11.  Colon Operator
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12.  The matrix indices begin from 1 (not 0 (as in C))
 The matrix indices must be positive integer
12

13.  Accessing Single Elements of a Matrix A(i,j)
 Accessing Multiple Elements of a Matrix
A(1,4) + A(2,4) + A(3,4) + A(4,4)
A([1,3,4], :)= all of rows 1, 3 and 4
sum(A(1:4,4))
sum(A(:,end))
The keyword end refers to the last row or column.
 Deleting Rows and Columns: to delete the second column
of X, use X(:,2) = []
 Concatenating Matrices A and B C=[A;B]
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14. 14

15. Logic--searching with find
 Find--searches for the truth (or not false)
› b=[1 0 -1 0 0];
› I=find(b)
I=1 3 b(I) is an array without zeros
› I=find(ones(3,1)*[ 1 2 3]==2)
I= 4 5 6
› [I,J]=find(ones(3,1)*[ 1 2 3]==2)
I= 1 2 3
J= 2 2 2
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16.  + addition
 - subtraction
 * multiplication
 ^ power
 ‘ complex conjugate transpose
 / right matrix division
same as right multiplication by divisor inverse
 left matrix division
same as left multiplication by divisor inverse
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17.  Scalar functions –
used for scalars
and operate
element-wise when
applied to a matrix
or vector
 e.g. sin cos
tan atan
asin log abs
anglesqrt
roundfloor
17

18.  Vector functions –
operate on vectors
returning scalar
value
 e.g. max min
mean prod
sum length
18

19.  Matrix functions –
perform operations
on matrices
 e.g. eye size
inv det eig
 X = ones(r,c) %
Creates matrix full
with ones
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20.  X = zeros(r,c) % Creates
matrix full with zeros
 A = diag(x) % Creates
squared matrix with vector
x in diagonal
 [r,c] = size(A) % Return
dimensions of matrix A
 B = rand(r,c) %creates a
matrix of random numbers.
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21.  + - * / % Standard operations
 .+ .- .* ./ % Wise addition, subtraction,…
 v = sum(A) % Vector with sum of columns
21

22. 22

23. 23

24.  Note that
It is better to
multiply
A*inv(B)
instead of
divide A/B
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25. 25
Command flipud flips the matrix in UP/DOWN direction.
Command fliplr flips the matrix in LEFT/RIGHT direction

26. 26

27. Some powerful matrix functions in Matlab
 X = A’ % Transposed matrix
(A transpose operation changes the column of a matrix into rows, and
rows into columns)
 X = inv(A) % Inverse matrix squared matrix
 X = pinv(A) % Pseudo inverse
 X = chol(A) % Cholesky decomp.
 d = det(A) % Determinant
 [X,D] = eig(A) % Eigenvalues and eigenvectors
 [Q,R] = qr(X) % QR decomposition
 [U,D,V] = svd(A) % singular value decomp
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28.  maxVal =
max(aaa)
% finds the
maximum
value for a
matrix.
28

29.  minVal =
min(aaa);
% finds the
minimum
value for a
matrix.
29

30.  colSum =
sum(aaa);
% finds the
sum of each
column
30

31.  If A is a matrix,
sum(A) treats the
columns of A as
vectors, returning
a row vector of
the sums of each
column.
 B = sum(A,dim)
sums along the
dimension of A
specified by
scalar dim.
31

32.  B = sort(A,’ascend/descend’) % sorts a matrix. Default is
ascending mode.
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33. 1. A is a row vector. The first element in A is 0, and the
value vary from 0 to 10 with increment of 2
2. B is row vector with six elements, and every variable
in B is 2.5
3. Calculate the value of C, which is equal to the sum of
A and B
4. Calculate the value of D, which is equal to the
element-by element multiplication between A and B
5. Change A(1,3) to 8.
6. Calculate E = A./B
33

34. 1. A=[1, 2.7, 8.9, -8, 4, 3.5]
2. B>0;
3. Return the sum and mean value of all the
elements in A.
4. Return the max value of all elements in A.
5. fix(A)
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35. 1. A=[1, 2.7, 8.9, -8, 4, 3.5; 6.5, 8.9, 5, -0.9,
3, 19] ;
2. Set every element in six column to be 0.7.
3. Remove the second column in A;
4. Return the mean value of every column in
A;
5. Return the mean value of whole A;
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