Episode: 1 Vectors, what even are they? Episode: 2 Linear combinations, span, and basis vectors Episode: 3 Linear transformations and matrices Episode: 4 Matrix multiplication as composition Episode: 5 Three-dimensional linear transformations Episode: 6 The determinant Episode: 7 Inverse matrices, column space and null space Episode: 8 Nonsquare matrices as transformations between dimensions Episode: 9 Dot products and duality Episode: 10 Cross products Episode: 11 Cross products in the light of linear transformations Episode: 12 Cramer's rule, explained geometrically Episode: 13 Change of basis Episode: 14 Eigenvectors and eigenvalues Episode: 15 A quick trick for computing eigenvalues Episode: 16 Abstract vector spaces