Matrix Calculations: Basis Change and Extensions

Related lectures (24)

Page 1 of 3

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Covers vector spaces, bases, and decomposition of vectors in R³.

Covers notations, operations, isomorphism, and polar decomposition of complex numbers.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores the Gauss representation of complex numbers, focusing on addition, multiplication, bases, and vector space dimensions.

Explores linear mapping, isomorphism, and change of bases in vector spaces.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.