Linear Algebra: Orthogonal Bases and Hermitian Forms

Related lectures (23)

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Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

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

Explores Sylvester's Theorem and the importance of orthogonal bases in linear algebra.

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

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

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Explores orthogonal vectors in a vector subspace and their dimension.

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

Explains kernel, image, and linear maps, illustrating concepts with examples.