Explanation:
Matrix
(mathematics)
Specific
elements of a matrix are often denoted by a variable with two subscripts. For
instance,a_{2,1} represents the element at the second row and first
column of a matrix A.
In mathematics, a matrix (plural matrices, or
less commonly matrixes) is a
rectangular array of numbers, symbols, or expressions. The individual items in
a matrix are called its elements or entries. An example
of a matrix with six elements is
http://en.wikipedia.org/wiki/Matrix_(mathematics)
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries
together. However, there is another operation which could also be considered as
a kind of addition for matrices.
The usual
matrix addition is defined for two matrices of the same dimensions. The sum of
two m-by-n matrices A and B, denoted by A + B, is again an m-by-n matrix computed by adding
corresponding elements. For example:
(Our solved example in
mathguru.com uses this concept)
We can also subtract one matrix
from another, as long as they have the same dimensions. A - B is
computed by subtracting corresponding elements of A and B,
and has the same dimensions as A and B. For
example:
http://en.wikipedia.org/wiki/Matrix_addition
Transpose
In linear algebra, the transpose of a matrix A is another matrix A^{T} (also written A′, A^{tr} or ^{t}A) created by any one of the following
equivalent actions:
1.
reflect A over its main diagonal (which runs top-left to bottom-right)
to obtain A^{T}
2.
write the rows of A as the columns of A^{T}
3.
write the columns of A as the rows of A^{T}
4.
visually rotate A 90 degrees clockwise, and mirror the
image in a vertical line to obtain A^{T}
Formally, the (i,j) element of A^{T} is the (j,i) element of A.
[A^{T}]_{ij} = [A]_{ji}
(Our
solved example in mathguru.com uses this concept)
If A is an m × n matrix then A^{T} is a n × m matrix.
The transpose of a scalar is the same scalar.
Examples
1.
2.
3.
http://en.wikipedia.org/wiki/Transpose
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.