MATH-115(b): Advanced linear algebra II

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Lectures in this course (43)

Eigenvalues and Eigenvectors

Covers eigenvalues, eigenvectors, and their applications in linear algebra.

Decomposition of Linear Operators

Covers the decomposition of linear operators and properties of eigenspaces.

Orthogonal Matrices and Eigenvalues

Explores orthogonal matrices, eigenvalues, and orientation-preserving transformations in linear algebra.

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Sylvester's Inertia Theorem

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Real Vector Spaces: Structure and Endomorphisms

Covers the structure of real vector spaces and endomorphisms.

Dual Bases: Canonical and Dual Spaces

Explores the concept of dual bases in linear algebra and their practical applications.

Linear Algebra: Matrix Operations and Applications

Covers matrix operations and their applications in linear algebra.

Eigenvalues and Eigenvectors

Covers the concept of eigenvalues and eigenvectors in linear algebra, focusing on the properties of endomorphisms.

Linear Recurrences and Applications

Explores linear recurrences, applications between sets, and the significance of functions and operators in mathematics and physics.

Decomposition Principle: Linear Algebra

Explores the decomposition principle in linear algebra, showing how a vector space can be split into two subspaces.

Modeling Heat Equation

Covers the modeling of the heat equation using Laplacian operator and Riemann varieties.

Linear Algebra: Decomposition Theorems

Covers the proof of primary decomposition theorem for endomorphisms of finite-dimensional vector spaces.

Dynamics of Discrete Systems

Covers the dynamics of discrete systems and the concept of orbits in Riemann varieties.

Galilean Transformations: Spacetime and Measurements

Explores Galilean transformations in spacetime, focusing on measurements and coordinate transformations.

Pseudo-Euclidean Spaces: Isometries and Bases

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Lorentz-Minkowski Spacetime

Covers Lorentz-Minkowski spacetime, speed of light interpretation, isometries, and special relativity principles.

Interpolation of Lagrange: Dualité and Coupling

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

Canonical Couplings in Linear Algebra

Explores canonical couplings in linear algebra, emphasizing their notation and usefulness in various applications.

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

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