Topic: Linear Maps Between Vector Spaces

Zero, Identity, Inclusion, and Projection Maps

Worked Classification of Polynomial-Space Maps

Worked Classification of Matrix and Function-Space Maps

Why Kernels and Images Are Subspaces

What Makes a Map Linear

Trace and Transpose on Matrix Spaces

The Rank-Nullity Theorem for Linear Maps

The Additivity-and-Homogeneity Test

Surjectivity and Full Image

Solving T(v)=w Using One Preimage and the Kernel