Linear Applications: Bases and Dual Spaces

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Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers the definitions and properties of dual spaces and linear operators.

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Explores the Kernel-Image Theorem, bijectivity conditions, linear forms, and surjectivity in linear algebra.

Explores properties of linear applications, including symmetric matrices and linearity in analysis.

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.