Fundamentals of Linear Algebra for University Students

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Your Gateway to Knowledge Science and Machine Studying Necessities by means of Mastering Vectors, Matrices and Tensors.

What you’ll be taught

Acquire data of vector areas and calculations

Acquire data of matrix properties and operations

Acquire data of eigenvalues and eigenvectors

Acquire data of tensor properties and operations

Description

Linear algebra isn’t nearly calculations, it’s a strong lens to see the world. This foundational course introduces college college students to the core rules of linear algebra, providing a complete exploration of elementary ideas and purposes. Designed to domesticate a powerful mathematical framework, the curriculum spans key subjects important for understanding vector areas, matrices, tensors and linear transformations. College students will delve into the mathematical constructions that underpin these ideas, gaining proficiency in operations equivalent to addition, multiplication, and inversion of matrices. The course locations a major emphasis on sensible problem-solving, thus guiding college students by means of the appliance of linear algebra in real-world eventualities, together with pc graphics, optimization, knowledge science and knowledge evaluation.

The exploration of eigenvalues and eigenvectors varieties an important element of the course, offering college students with a deeper understanding of diagonalization and its various purposes throughout disciplines. By a mix of theoretical instruction and hands-on workouts, college students will be capable of develop analytical abilities and significant pondering that enables them to strategy complicated issues with confidence.

Upon completion, college students will possess a strong basis in linear algebra, equipping them for superior coursework in arithmetic, pc science, physics, engineering, and numerous different fields the place linear algebra performs a pivotal function.

English
language

Content material

Introduction

Introduction

Vectors – Introduction

Scalar vs. Vector
Vectors Fundamentals

Vectors – Magnitude and Course

Magnitude and Course – Introduction
Magnitude and Course – Instance 1
Magnitude and Course – Instance 2

Vectors – Properties

Properties – Introduction
Properties – Instance 1
Properties – Instance 2
Properties – Instance 3

Vectors – Bases

Bases

Vectors – Unit Vectors

Unit Vectors – Introduction
Unit Vectors – Instance

Vectors – 3D Vectors

3D Vectors – Introduction
3D Vectors – Instance

Vectors – Collinearity in Vectors

Collinearity in Vectors – Introduction
Collinearity in Vectors – Instance 1
Collinearity in Vectors – Instance 2
Collinearity in Vectors – Instance 3
Collinearity in Vectors – Instance 4

Vectors – Dot Product

Dot Product – Introduction
Dot Product – Instance 1
Dot Product – Instance 2
Dot Product – Instance 3

Vectors – Dot Product Makes use of

Dot Product Makes use of – Introduction
Dot Product Makes use of – Instance 1
Dot Product Makes use of – Instance 2
Dot Product Makes use of – Instance 3

Vectors – Cross Product

Cross Product – Introduction
Cross Product – Instance

Vectors – Vectors Differentiation

Vectors Differentiation – Introduction
Vectors Differentiation – Instance 1
Vectors Differentiation – Instance 2
Vectors Differentiation – Instance 3
Vectors Differentiation – Instance 4

Vectors – Vectors Partial Differentiation

Vectors Partial Differentiation – Introduction
Vectors Partial Differentiation – Instance

Vectors – Vectors Integration

Vectors Integration – Introduction
Vectors Integration – Instance 1
Vectors Integration – Instance 2
Vectors Integration – Path Integrals

Vectors – Vectors Double Integration

Vectors Double Integration – Introduction
Vectors Double Integration – Instance

Vectors – Scalar Fields and Vector Fields

Scalar Fields vs. Vector Fields
Scalar Subject Gradient – Introduction
Scalar Subject Gradient – Instance
Scalar Subject Laplacian – Introduction
Scalar Subject Laplacian – Instance
Vector Filed Divergence – Introduction
Vector Filed Divergence – Instance
Vector Filed Curl – Introduction
Vector Filed Curl – Instance
Vector Subject Laplacian – Introduction
Vector Subject Laplacian – Instance

Matrices – Introduction

Matrices Fundamentals
Matrices Guidelines – Introduction
Matrices Guidelines – Instance 1
Matrices Guidelines – Instance 2

Matrices – Commutator

Commutator – Introduction
Commutator – Instance

Matrices – Matrix Operations

Matrix Operations – Introduction
Matrix Hint – Introduction
Matrix Hint – Instance 1
Matrix Hint – Instance 2
Matrix Transpose – Introduction
Matrix Transpose – Instance
Matrix Complicated Conjugate – Introduction
Matrix Complicated Conjugate – Instance
Matrix Hermitian Complicated Conjugate – Introduction
Matrix Hermitian Complicated Conjugate – Instance

Matrices – Matrix Determinant

Matrix Determinant – Introduction
Matrix Determinant – Properties
Matrix Determinant – Instance 1
Matrix Determinant – Instance 2

Matrices – Matrix Inverse

Matrix Inverse – Introduction
Matrix Inverse – Instance
Matrix Inverse – Matrix Inverse to Remedy Algebraic Equations

Matrices – Eigenvalues and Eigenvectors

Eigenvalues and Eigenvectors – Introduction
Eigenvalues and Eigenvectors – Instance

Matrices – Matrix Diagonalization

Matrix Diagonalization – Introduction
Matrix Diagonalization – Instance 1
Matrix Diagonalization – Instance 2
Matrix Diagonalization – Instance 3

Tensors – Introduction

Tensors – Introduction
Tensors – Covariant vs. Contravariant Tensors

Tensors – Tensors Addition

Tensors Addition – Introduction
Tensors Addition – Instance

Tensors – Tensors Contraction

Tensors Contraction – Introduction
Tensors Contraction – Instance 1 (Dot Product)
Tensors Contraction – Instance 2 (Hint)

Tensors – Tensors Enlargement

Tensors Enlargement – Tensors Multiplication (Dyad Product) – Introduction
Tensors Enlargement – Tensors Multiplication (Dyad Product) – Instance
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