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Example:Verify Property of Transpose

 Post to:   Explanation:

Matrix (mathematics) Specific elements of a matrix are often denoted by a variable with two subscripts. For instance,a2,1 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: # Transpose

In linear algebra, the transpose of a matrix A is another matrix AT (also written A′, Atr or tA) 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 AT

2.  write the rows of A as the columns of AT

3.  write the columns of A as the rows of AT

4.  visually rotate A 90 degrees clockwise, and mirror the image in a vertical line to obtain AT

Formally, the (i,j) element of AT is the (j,i) element of A.

[AT]ij = [A]ji

(Our solved example in mathguru.com uses this concept)

If A is an m × n matrix then AT is a n × m matrix. The transpose of a scalar is the same scalar.

## Examples

1. 2. 3. http://en.wikipedia.org/wiki/Transpose