# Linear Algebra

### Quadratic Form in Linear Algebra

Quadratic Form in Linear Algebra An expression is called quadratic form in the variables x1, x2, x3,………….,xn over field F. Where aij i=1,2,3,….n, j=1,2,3,….m are elements of F. If aij are real then quadratic form…

### Matrix Representation of a Linear Transformation

Matrix Representation of a Linear Transformation Suppose U and V are two vector spaces over the same field F of dimensions m and n. Let A = {α1, α2, α 3,……,α3} and B={β1, β2, β3,…….,βn}…

### Caley-Hamilton Theorem

To  understand  Caley-Hamilton theorem you have to know about characteristic polynomial. Characteristic Polynomial If A is a square matrix of of size n * n, and I is identity matrix of the same size as…

### Vector Spaces and Linear Transformation

Vector Space- A set V is called vector space on which two operations are defined. 1- Vector Addition 2- Scalar Multiplication Further, vector addition must follow the following properties and laws for vector addition. 1-…

### Linear Dependence and Independence of Vectors

Linear  Independence of Vectors Suppose α1, α2, α3, α4…………αn are vectors  of V(F) where F is field.  And there exist scalers a1, a2, a3, a4………..an which belong to field F. α1, α2, α3, α4…………αn vectors…