Linear Algebra

Matrix of a Quadratic Form in 3 Variables

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…




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-…


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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…