Lectures related to Bases in Known Dimension Space

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Covers orthogonal families and projections in vector spaces, including the Gram-Schmidt process.

Covers the properties and criteria of linear dependence and independence in a vector space.

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

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Revisits line and column ranks in matrices, demonstrating their equality and properties.