%%visits: 2 The dimension of a space or linear transformation is how many vectors are in a basis of the range. $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$ has dimension 3 $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}$ has dimension 2 ## intuition Think about orthogonality, basis that cannot interact with each other. A [[basis]] is the maximum numbber of vectors that are orthogonal to each other. ## rigour ## exam clinic ## resources tags :math:linear_algebra_1:linear_algebra_2: