Vector Spaces

Explore the fundamental concepts of vector spaces in linear algebra through 25 illustrative examples. Delve into subspaces, unions of subspaces, and spans, while mastering key theorems such as the Intruder Theorem and Replacement Theorem. Investigate the properties of direct sums, dimensions, and infinite-dimensional spaces. Learn about Lagrange Interpolation and gain insight into Zorn's Lemma and its application to basis theory. This comprehensive 4.5-hour lecture provides a solid foundation in vector space theory, essential for advanced mathematics and its applications.

linear algebra vector space (25 examples).
Subspace.
Not subspace.
Union of subspaces.
Span is a subspace.
Intruder Theorem.
Direct Sum.
Dim Sum.
What is a dimension ?.
Replacement Theorem.
Replacement Theorem Proof.
Infinite dimensions.
Lagrange Interpolation.
Zorn’s Lemma and Basis.