Matrix Interpretation

Matrix as Linear Transformation

• Any matrix-vector product is essentially a linear transformation.

• Any linear transformation can be seen as a change of basis as well.

• So matrix multiplication is basically a linear transformation of a vector or change of basis.

$A^Tb$ where $A$is a matrix and $b$is a vector, denotes the projection of $b$ on the columns space of $A$.

Matrix as a Projection

Two Forms of the Dot Product