Linear Algebra Basics

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Related lectures (23)

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Linear Algebra: Compositions and Injections

Explores compositions and injections in linear algebra, emphasizing their importance.

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Linear Algebra in 3D: Images and Kernels

Explores linear applications in 3D, emphasizing images, kernels, and solution uniqueness in systems.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Algebra: Integers

Explores linear algebra over integers, emphasizing solutions to A.x=b equations and Hermite normal form.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.