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

Lectures in this course (60)

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

Covers the base change matrix, transition matrix, and equivalence of matrices in linear algebra.

Explores matrices conjugation, equivalence, and similarity in advanced linear algebra.

Covers the basics of solving polynomial equations, historical methods, matrix properties, imaginary numbers, and subrings in matrix algebras.

Covers the properties of the algebra of matrices and related concepts.

Covers matrix calculations, basis change, field extensions, complex numbers modulus, and polar decomposition.

Explores complex numbers, trigonometric functions, De Moivre's formulas, and complex plane representation.

Explores the properties and applications of Euclidean isometries in R^2.

Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Explores elementary matrices, operations, equivalence, and echelons in matrices.

Explores the properties and uniqueness of reduced echelon matrices and the criterion of invertibility.

Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Introduces multilinear forms in linear algebra, emphasizing clarity and logic in presentation.

Covers multilinear forms in n variables over a k-vector space, emphasizing notation and applications.

Explores permutations, signature, and alternating multilinear forms in vectors.

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Explores symmetric formulas and properties of determinants, including invertibility and matrix calculations.

Explores the properties and applications of determinants of matrices in linear algebra.

Covers the expansion theorems for determinants and introduces Cramer's formula.

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