Matrix

You can free download topic by Matrix in pdf format. Matrix In the mathematics , a matrix is a rectangular array of numbers,symbols or e...

You can free download topic by Matrix in pdf format.

Matrix

In the mathematics , a matrix is a rectangular array of numbers,symbols or expressions , arranged in rows and columns.For example, the dimension f the matrix below is 2 x 3 ,because there are two rows and three columns:provided that they have the same size and two matrix can be added or subtracted  elements by elements ( See conformable matrix ).the rule for Matrix Multiplication,however ,is that two matrices can be multiplied only when the number of columns in the first equals the number of the rows in the second (i.e the inner dimension are the same ,n for an (m ｘ n)-matrix times an (n ｘ p )- matrix ,resulting resulting  in an (m🗙p )- matrix ).There is no product the other way round, a first hint that matrix multiplication is not commutative. 

Any matrix can be multiplied element-wise by a scalar from its associated field.The individual items in an m🗙n matrix A.Any matrix cannot be multiplied its.A major application of matrices is to represent linear transformation,that is ,generalizations of linear function,such as f(x)=4x. For example ,the rotation of vectors in the three dimensional space is a linear transformation ,which can be represented by a rotation matrix R.IF V is a column vector ( a matrix with only  one column )describing the position of a point in space ,the product RV is a columns vector .The product of two transformation matrix is a matrix that represents the composition of two transformations.Another application of matrices is in the solution of system of linear equations.

if matrix is square ,it is possible to deduce some of its properties by computing its determinant.For example , a square matrix has an inverse if and only if its determinant is not zero . insight into the geometry of a linear transformation is obtainable (along with other information )from the matrix's eigenvalues and eigenvectors.