Biology Reference
In-Depth Information
4)
Square symmetric matrix:
A square matrix of dimension
m
m
is said to be symmetric if and only if
a
ij
= a
ji
for all
i = 1,2,..,m;
j = 1,2,...,m.
For example,
is a 3 x 3 square, symmetric matrix.
5)
Definition of a vector:
A matrix that has only one column and
has dimension
m
1
, is called a vector. Sometimes this is also
called a column vector. We denote a vector
V
of length
m
by
V= [v
i
]
i=1,2,…m
.
For example,
is a vector of length 3. Also notice that, in this
example,
v
1
= 1,v
2
= 2
and
v
3
= 3
.
6)
Transpose of a matrix:
The transpose of a matrix is a matrix
obtained by turning columns of the original matrix into rows
while keeping their original order. The transpose of a matrix
A
is denoted by
A
T
.
For example, if then
The transpose of a column vector is called a row vector.
7)
Equality of two matrices:
Two matrices
A
and
B
are said to be
equal to each other if, and only if, they have the same dimen-
sion and
a
ij
= b
ij
for every
i
and
j
. That is, if and only if all of
the corresponding elements are identical.
2.6.1 Addition and multiplication of matrices
Matrices do not behave like ordinary numbers. Addition and multipli-
cation of matrices are allowed only if the matrices conform to certain
dimensional restrictions.
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