MATH-110(a): Advanced linear algebra I - vector spaces

Lectures in this course (60)

Explores module generation, submodules, modulus, finite type modules, and morphisms.

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.

Covers advanced topics in linear algebra, including finite fields, invertible matrices, and vector spaces.

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

Introduces injective morphisms and vector spaces with examples and verification methods.

Discusses linear applications between vector spaces and properties of endomorphisms and automorphisms.

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

Explores isomorphic structures, base canonique, invertible elements, and constructing smallest sev in vector spaces.

Discusses generating families in vector spaces and conditions for linked or free families.

Explores bases in vector spaces, including extraction from incomplete families and the concept of vector subspaces like lines and planes.

Explores dimension theory of vector spaces, covering bases, linear applications, and ranks.

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

Explores the dimension of linear maps and the construction of bases.

Explores linear maps, basis freedom, composition, coordinates in different bases, associated matrices, and coefficients.

Explores bases, dual spaces, and linear applications in linear algebra.

Explores Theorem 7.6 on the rank of the dual map in linear applications and delves into matrices and scalar matrices.

Covers matrix operations, linear forms, and bases in mathematics, emphasizing their significance.

Explores canonical forms of matrices, matrix products, and linear applications in vector spaces.

Covers the definition of associated matrices, matrix products, image vectors, and isomorphisms.

Explores elementary linear algebra concepts related to matrices, including invertible connections and matrix rank.

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