Graphics Programs Reference
In-Depth Information
You can use MATLAB to do computations involving complex numbers by en-
tering numbers in the form
a + b*i
:
>> (2 + 3*i)*(4 - i)
ans =
11.0000 + 10.0000i
Complex arithmetic is a powerful and valuable feature. Even if you don't in-
tend to use complex numbers, you should be alert to the possibility of complex-
valued answers when evaluating MATLAB expressions.
More on Matrices
In addition to the usual algebraic methods of combining matrices (e.g., matrix
multiplication), we can also combine them element-wise. Specifically, if
A
and
B
are the same size, then
A.*B
is the
element-by-element
product of
A
and
B
,
that is, the matrix whose
i
,
j
element is the product of the
i
,
j
elements of
A
and
B
.Likewise,
A./B
istheelement-by-elementquotientof
A
and
B
,and
A.ˆc
is the matrix formed by raising each of the elements of
A
to the power
c
. More
generally, if
f
is one of the built-in functions in MATLAB, or is a user-defined
function that accepts vector arguments, then
f(A)
is the matrix obtained
by applying
f
element-by-element to
A
. See what happens when you type
sqrt(A)
, where
A
is the matrix defined at the beginning of the
Matrices
section of Chapter 2.
Recall that
x(3)
is the third element of a vector
x
. Likewise,
A(2,3)
rep-
resents the 2
,
3 element of
A
, that is, the element in the second row and third
column. You can specify submatrices in a similar way. Typing
A(2,[2 4])
yields the second and fourth elements of the second row of
A
. To select the
second, third, and fourth elements of this row, type
A(2,2:4)
. The subma-
trix consisting of the elements in rows 2 and 3 and in columns 2, 3, and 4 is
generated by
A(2:3,2:4)
. A colon by itself denotes an entire row or column.
For example,
A(:,2)
denotes the second column of
A
, and
A(3,:)
yields the
third row of
A
.
MATLAB has several commands that generate special matrices. The com-
mands
zeros(n,m)
and
ones(n,m)
produce
n
×
m
matricesofzerosandones,
respectively. Also,
eye(n)
represents the
n
×
n
identity matrix.
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