Vector Space

Vector Space

1. Linear Independence

2. Linear Span

3. Ax=b

4. Vector Subspace

   • Finite Dimensional Spaces
     • Basis / Base
       • Ordered, spanning set of linear independent vectors.
         • Change Base

5. Square Matrix

   • - Inverse of A exists.
   • Determinant is non zero
   • Rows of A are linearly independent.
   • x zero row after row reduction
   • rank(A) + nullity(A) = dim-dom A
     • Kernel(T) = Null Space
       • T(u) = 0
     • Range Space = Image Space
       • T(u) =v
   • scalar

6. Linear Transformations

   • Eg. Matrix Transformation

7. Inner Product Space