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Linear Algebra

  • Course level: Beginner
  • Categories C-Science
  • Last Update 23/06/2021

Description

In this course, We will explain the essentials of Linear Algebra (LA) and everything that you need to understand the basics of linear algebra. We will cover content such as:

  1. Matrices and Linear System of Equations
  2. Gaussian Elimination
  3. Reduced Echelon Form and RREF
  4. Matrix Algebra
  5. Special Matrices, Diagonal Matrices, and Inverse Matrices
  6. Inverse Matrices and The Inverses of Transposed Matrices
  7. Determinants and computing the Determinant
  8. Much more!

By the end of this course, you should very comfortable with linear algebra and be able to follow throw any Math which uses the (LA) notation.

You will also get answers to any questions on any (LA) questions that you might have for life. 

Who this course is for:

  1. Computer Science Students Who Want To Learn More
  2. Students Who Want To Learn The (LA) For Machine Learning and Deep Learning
  3. Anyone Who Is Interested In Math And Wants To Study (LA)

What Will I Learn?

  • You will learn an introduction to linear algebra
  • You will learn the matrix types
  • You will learn the determinants
  • You are a student of eigen vectors
  • At the end of my course, students will be able to understand the basic fundamentals and principles of algebra.

Topics for this course

82 Lessons

Linear Algebra

What’s the big idea of Linear Algebra?00:00:00
What is a Solution to a Linear System?00:00:00
Visualizing Solutions to Linear Systems00:00:00
Rewriting a Linear System using Matrix Notation00:00:00
Using Elementary Row Operations to Solve Systems of Linear Equations00:00:00
Using Elementary Row Operations to simplify a linear system00:00:00
Examples with 0, 1, and infinitely many solutions to linear systems00:00:00
Row Echelon Form and Reduced Row Echelon Form00:00:00
Back Substitution with infinitely many solutions00:00:00
What is a vector?00:00:00
Introducing Linear Combinations & Span00:00:00
How to determine if one vector is in the span of other vectors?00:00:00
Matrix-Vector Multiplication and the equation Ax=b00:00:00
Matrix-Vector Multiplication Example00:00:00
Proving Algebraic Rules in Linear Algebra — Ex: A(b+c) = Ab +Ac00:00:00
The Big Theorem, Part I00:00:00
Writing solutions to Ax=b in vector form00:00:00
Geometric View on Solutions to Ax=b and Ax=0.00:00:00
Three nice properties of homogeneous systems of linear equations00:00:00
Linear Dependence and Independence – Geometrically00:00:00
Determining Linear Independence vs Linear Dependence00:00:00
Making a Math Concept Map | Ex: Linear Independence00:00:00
Transformations and Matrix Transformations00:00:00
Three examples of Matrix Transformations00:00:00
Linear Transformations00:00:00
Are Matrix Transformations and Linear Transformation the same? Part I00:00:00
Every vector is a linear combination of the same n simple vectors!00:00:00
Matrix Transformations are the same thing as Linear Transformations00:00:00
Finding the Matrix of a Linear Transformation00:00:00
One-to-one, Onto, and the Big Theorem Part II00:00:00
The motivation and definition of Matrix Multiplication00:00:00
Computing matrix multiplication00:00:00
Visualizing Composition of Linear Transformations00:00:00
Elementary Matrices00:00:00
You can “invert” matrices to solve equations…sometimes!00:00:00
Finding inverses to 2×2 matrices is easy!00:00:00
Find the Inverse of a Matrix00:00:00
When does a matrix fail to be invertible? Also more “Big Theorem”.00:00:00
Visualizing Invertible Transformations (plus why we need one-to-one)00:00:00
Invertible Matrices correspond with Invertible Transformations **proof**00:00:00
Determinants – a “quick” computation to tell if a matrix is invertible00:00:00
Determinants can be computed along any row or column – choose the easiest!00:00:00
Vector Spaces | Definition & Examples00:00:00
The Vector Space of Polynomials: Span, Linear Independence, and Basis00:00:00
Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples00:00:00
The Span is a Subspace | Proof + Visualization00:00:00
The Null Space & Column Space of a Matrix | Algebraically & Geometrically00:00:00
The Basis of a Subspace00:00:00
Finding a Basis for the Nullspace or Column space of a matrix A00:00:00
Finding a basis for Col(A) when A is not in REF form.00:00:00
Coordinate Systems From Non-Standard Bases | Definitions + Visualization00:00:00
Writing Vectors in a New Coordinate System **Example**00:00:00
What Exactly are Grid Lines in Coordinate Systems?00:00:00
The Dimension of a Subspace | Definition + First Examples00:00:00
Computing Dimension of Null Space & Column Space00:00:00
The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank!00:00:00
Changing Between Two Bases | Derivation + Example00:00:00
Visualizing Change Of Basis Dynamically00:00:00
Example: Writing a vector in a new basis00:00:00
What eigenvalues and eigenvectors mean geometrically00:00:00
Using determinants to compute eigenvalues & eigenvectors00:00:00
Example: Computing Eigenvalues and Eigenvectors00:00:00
A range of possibilities for eigenvalues and eigenvectors00:00:00
Diagonal Matrices are Freaking Awesome00:00:00
How the Diagonalization Process Works00:00:00
Compute large powers of a matrix via diagonalization00:00:00
Full Example: Diagonalizing a Matrix00:00:00
COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**00:00:00
Visualizing Diagonalization & Eigenbases00:00:00
Similar matrices have similar properties00:00:00
The Similarity Relationship Represents a Change of Basis00:00:00
Dot Products and Length00:00:00
Distance, Angles, Orthogonality and Pythagoras for vectors00:00:00
Orthogonal bases are easy to work with!00:00:00
Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Compliment00:00:00
The geometric view on orthogonal projections00:00:00
Orthogonal Decomposition Theorem Part II00:00:00
Proving that orthogonal projections are a form of minimization00:00:00
Using Gram-Schmidt to orthogonalize a basis00:00:00
Full example: using Gram-Schmidt00:00:00
Least Squares Approximations00:00:00
Reducing the Least Squares Approximation to solving a system00:00:00
50 £

Enrolment validity: Lifetime

Requirements

  • Internet connection
  • A strong learning