Topic: Linear Transformations of R^n

Why Every Linear Transformation Has One Standard Matrix

Why Composition Multiplies Standard Matrices

The Null Space Test for One-to-One Transformations

The Column Space Test for Onto Transformations

Testing Whether a Formula Is Linear

Standard Matrices from Basis-Vector Images

Shear Transformations and Their Standard Matrices

Rotation and Uniform Scaling Matrices in the Plane

Recovering a Matrix from Transformation Constraints

Proving the Pivot-Row Criterion for Surjectivity