Vector Spaces
Definition of a Vector Space
Examples
Example 1: is a vector space over (column vectors).
Example 2: (polynomials) is a vector space over .
Example 3: (matrices) is a vector space over .
Example 4: (continuous functions) is a vector space over .
Subspaces
Subspace Test
Linear Combinations
Span
Linear Independence
Null Space and Column Space
For a matrix :
Both are subspaces.