Lectures related to Null vector

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Explores Weyl characters, Macdonald's identities, and Borcherds products in Euclidean space.

Covers important examples related to operations and multiplication in real vector spaces.

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Introduces the kernel of a linear application and its properties.

Explores quadratic forms, symmetries, representations, and orthogonal sums in mathematics.

Covers local fields and correlations in Ising models and conformal field theory.

Covers examples of vector spaces and the concept of subspaces, emphasizing key properties and verification methods.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Explores the scalar product of vectors, including properties and calculation methods.

Introduces eigenvalues and eigenvectors for square matrices through examples.

Explores vector subspaces and linear combinations in linear algebra, focusing on the reciprocal relationship between lines, columns, and elements.

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

Explores rectilinear movement, vector algebra, scalar products, and vector decomposition in a three-dimensional space.

Explores linear transformations, matrices, kernels, and images in algebra.

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Covers examples of stable vector subspaces and how to find eigenvalues.

Covers the representation and operations in coordinate space with points and vectors.

Explains matrix trace properties and finding independent vectors in trace space.