Real Vector Spaces: Structure and Endomorphisms

Related lectures (30)

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Introduces vector spaces, linear applications, generators, and dimensionality in mathematics.

Covers the basics of finite fields, including arithmetic operations and properties.

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

Explores properties of matrices, endomorphisms, and linear applications in vector spaces.

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

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

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

Explores matrix representation of linear applications, emphasizing eigenvalues and bases.

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.