Page 32 - Applied Numerical Methods Using MATLAB

BASIC OPERATIONS OF MATLAB 21
Remark 1.3. More Useful Commands for Vector/Matrix Operations

1. We can use the commands zeros(), ones(),and eye() to construct a
matrix of specified size or the same size as an existing matrix which has
only zeros, only ones, or only ones/zeros on/off its diagonal.
>>Z = zeros(2,3) %or zeros(size(A1)) yieldinga2x3 zero matrix
Z = 0 0 0
0 0 0
>>E = ones(size(B)) %or ones(3,2) yieldinga3x2one matrix
E=1 1
1 1
1 1
>>I = eye(2) %yieldinga2x2 identity matrix
I=1 0
0 1
2. We can use the diag() command to make a column vector composed
of the diagonal elements of a matrix or to make a diagonal matrix with
on-diagonal elements taken from a vector given as the input argument.
>>A1, diag(A1) %column vector consisting of diagonal elements
A1 = -1 2 3
4 5 2
ans=-1
5

3. We can use the commands sum()/prod() to get the sum/product of ele-
ments in a vector or a matrix, columnwisely first (along the first non-
singleton dimension).
>>sa1 = sum(a1) %sum of all the elements in vector a 1

sa1=4% a 1 (n) =− 1 + 2 + 3 = 4
>>sA1 = sum(A1) %sum of all the elements in each column of matrix A 1

M
sA1=3 7 5 %sA1(n) = m = 1 A 1 (m, n) = [− 1 + 4 2 + 5 3 + 2]
>>SA1 = sum(sum(A1)) %sum of all elements in matrix A 1

N
M
SA1=15 %SA1 = A 1 (m, n) = 3 + 7 + 5 = 15
n = 1 m = 1
>>pa1 = prod(a1) %product of all the elements in vector a 1

pa1=4% a 1 (n) = ( − 1) × 2 × 3 =− 6
>>pA1=product(A1) %product of all the elements in each column of matrix A 1
M
pA1=-4 10 6 %pA1(n) = m = 1 A 1 (m, n) = [−1 × 4 2 × 5 3 × 2]
>>PA1 = product(product(A1)) %product of all the elements of matrix A 1
N M
PA1 = -240 %PA1 = n = 1 m = 1 A 1 (m, n) = ( − 4) × 10 × 6 =− 240
4. We can use the commands max()/min() to find the first maximum/minimum
number and its index in a vector or in a matrix given as the input argument.
>>[aM,iM] = max(a2)
aM = 5, iM = 2 %means that the max. element of vector a2 is a2(2) = 5
>>[AM,IM] = max(A1)
AM = 4 5 3
IM = 2 2 1
%means that the max. elements of each column of A1 are
A1(2,1) = 4, A1(2,2) = 5, A1(1,3) = 3