Module: Linear Spaces

Learning Outcomes

Linear Spaces

• You understand what “closed under linear combinations” means
• You know what a linear space is
• You know the 4 fundamental spaces of a matrix: the row, column, left and right null spaces
• \(\textrm{col}(A) = \{ A{\bf x} : \textrm{ all values of }{\bf x} \}\) (column)
• \(\textrm{null}(A) = \{ {\bf x} : A{\bf x} = {\bf 0} \}\) (right null)
• row space of \(A\) \(=\) col space of \(A^T\)
• left null space of \(A\) \(=\) right null space of \(A^T\)
• If \(A\) is \(m\times n\), number of coordinates of vectors in each of the spaces

Readings

Experiential Learning