Examples:
Simple Vector Algebra

On
this page
we expose how simple it is to work with vector algebra, within Matlab.
Reproduce this example in MATLAB:
x = [2 4 6 8];
y = 2*x + 3
y = 7
11
15 19
Row
vector
y
can represent a straight line by doubling the x value
(just as
a slope = 2) and adding a constant.

Something
like y = mx +
c. It's
easy to perform algebraic operations on vectors since you apply the
operations to the whole vector, not to each element alone.
Now, let's create two row
vectors (v
and w),
each with 5 linearly
spaced elements (that's easy with function 'linspace'):
v = linspace(3, 30, 5)
w = linspace(4, 400, 5)
Obtain a row vector containing the sine
of each element
in v:
x = sin(v)
Multiply these elements by their correspondig element in vector w:
y = x .* w
And obtain MATLAB's response:
y =
0.5645 32.9105 143.7806
286.4733 395.2126
>>
Did you obtain the same? Results don't appear on screen if you end the
command with the ';' sign.
y = x .* w;
You can create an array
(or matrix)
by combining two or more vectors:
m = [x; y]
The first row of m
above is x,
the second row is y.
m =
0.1411
0.3195 0.7118
0.9517 0.9880
0.5645 32.9105 143.7806
286.4733 395.2126
>>
You can refer to each
element of m by using subscripts.
For example,
m(1,2) = 0.3195 (first row, second column);
m(2,1) = 0.5645 (second
row, first column).
You can manipulate single elements of a matrix, and replace them on the
same matrix:
m(1,2) = m(1,2)+3
m(2,4) = 0
m(2,5) = m(1,2)+m(2,1)+m(2,5)
m =
0.1411
2.6805 0.7118
0.9517 0.9880
0.5645 32.9105
143.7806
0 391.9677
>>
Or you can perform algebraic operations on the whole matrix (using
elementbyelement operators):
z = m.^2
z =
1.0e+005 *
0.0000
0.0001
0.0000
0.0000 0.0000
0.0000
0.0108
0.2067
0 1.5364
>>
MATLAB automatically presents a coefficient
before the matrix, to
simplify the notation. In this case .
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'Vector Algebra' to
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'Vector
Algebra' to 'Matlab Examples'

