Biology Reference
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For example,
is a matrix.
2)
Dimension of a matrix: A matrix with m rows and n columns
is said to have dimensions m
n and is referred to as an
m
n matrix. We read it as “m by n matrix”. In text, we may
either write an m
n matrix, or interchangeably, an m by n
matrix.
The above matrix A is a 2 x 3 matrix. This matrix has 2 rows and 3
columns. Notice that this matrix has 6 elements. The number of ele-
ments in a matrix equals the product of the number of rows and the
number of columns.
As in ordinary algebra, we use symbols to identify the elements of
a matrix. In our applications the rows are represented by the symbol,
i , while columns are represented by the symbol j .
An element is identified by its location in the matrix according to
its row and column location. Thus, a ij refers to the element in the i -th
row and j -th column. For example, a 12 is the element in the first row
and second column. We read it as “a sub one two” or, if the context is
clear, simply as “a one two”. A commonly used short notation for a
matrix is A= [ a ij ] i=1,2,...,m;j=1,2,...,n or simply A= [ a ij ] if the range of the
subscripts is obvious from the context. For notational convenience, we
generally use the second notation.
For example, for the matrix, A
the element a 13 = 3
3)
Square matrix: A matrix is said to be square if the number of
rows equals the number of columns.
For example,
is a square matrix. This matrix
has 3 rows and 3 columns. Also notice that this has a total of 9 elements.
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