Linear Algebra

By ResearcherStore Categories: C-Science
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About Course

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)
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What Will You 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.

Course Content

Linear Algebra

  • What’s the big idea of Linear Algebra?
    00:00
  • What is a Solution to a Linear System?
    00:00
  • Visualizing Solutions to Linear Systems
    00:00
  • Rewriting a Linear System using Matrix Notation
    00:00
  • Using Elementary Row Operations to Solve Systems of Linear Equations
    00:00
  • Using Elementary Row Operations to simplify a linear system
    00:00
  • Examples with 0, 1, and infinitely many solutions to linear systems
    00:00
  • Row Echelon Form and Reduced Row Echelon Form
    00:00
  • Back Substitution with infinitely many solutions
    00:00
  • What is a vector?
    00:00
  • Introducing Linear Combinations & Span
    00:00
  • How to determine if one vector is in the span of other vectors?
    00:00
  • Matrix-Vector Multiplication and the equation Ax=b
    00:00
  • Matrix-Vector Multiplication Example
    00:00
  • Proving Algebraic Rules in Linear Algebra — Ex: A(b+c) = Ab +Ac
    00:00
  • The Big Theorem, Part I
    00:00
  • Writing solutions to Ax=b in vector form
    00:00
  • Geometric View on Solutions to Ax=b and Ax=0.
    00:00
  • Three nice properties of homogeneous systems of linear equations
    00:00
  • Linear Dependence and Independence – Geometrically
    00:00
  • Determining Linear Independence vs Linear Dependence
    00:00
  • Making a Math Concept Map | Ex: Linear Independence
    00:00
  • Transformations and Matrix Transformations
    00:00
  • Three examples of Matrix Transformations
    00:00
  • Linear Transformations
    00:00
  • Are Matrix Transformations and Linear Transformation the same? Part I
    00:00
  • Every vector is a linear combination of the same n simple vectors!
    00:00
  • Matrix Transformations are the same thing as Linear Transformations
    00:00
  • Finding the Matrix of a Linear Transformation
    00:00
  • One-to-one, Onto, and the Big Theorem Part II
    00:00
  • The motivation and definition of Matrix Multiplication
    00:00
  • Computing matrix multiplication
    00:00
  • Visualizing Composition of Linear Transformations
    00:00
  • Elementary Matrices
    00:00
  • You can “invert” matrices to solve equations…sometimes!
    00:00
  • Finding inverses to 2×2 matrices is easy!
    00:00
  • Find the Inverse of a Matrix
    00:00
  • When does a matrix fail to be invertible? Also more “Big Theorem”.
    00:00
  • Visualizing Invertible Transformations (plus why we need one-to-one)
    00:00
  • Invertible Matrices correspond with Invertible Transformations **proof**
    00:00
  • Determinants – a “quick” computation to tell if a matrix is invertible
    00:00
  • Determinants can be computed along any row or column – choose the easiest!
    00:00
  • Vector Spaces | Definition & Examples
    00:00
  • The Vector Space of Polynomials: Span, Linear Independence, and Basis
    00:00
  • Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples
    00:00
  • The Span is a Subspace | Proof + Visualization
    00:00
  • The Null Space & Column Space of a Matrix | Algebraically & Geometrically
    00:00
  • The Basis of a Subspace
    00:00
  • Finding a Basis for the Nullspace or Column space of a matrix A
    00:00
  • Finding a basis for Col(A) when A is not in REF form.
    00:00
  • Coordinate Systems From Non-Standard Bases | Definitions + Visualization
    00:00
  • Writing Vectors in a New Coordinate System **Example**
    00:00
  • What Exactly are Grid Lines in Coordinate Systems?
    00:00
  • The Dimension of a Subspace | Definition + First Examples
    00:00
  • Computing Dimension of Null Space & Column Space
    00:00
  • The Dimension Theorem | Dim(Null(A)) + Dim(Col(A)) = n | Also, Rank!
    00:00
  • Changing Between Two Bases | Derivation + Example
    00:00
  • Visualizing Change Of Basis Dynamically
    00:00
  • Example: Writing a vector in a new basis
    00:00
  • What eigenvalues and eigenvectors mean geometrically
    00:00
  • Using determinants to compute eigenvalues & eigenvectors
    00:00
  • Example: Computing Eigenvalues and Eigenvectors
    00:00
  • A range of possibilities for eigenvalues and eigenvectors
    00:00
  • Diagonal Matrices are Freaking Awesome
    00:00
  • How the Diagonalization Process Works
    00:00
  • Compute large powers of a matrix via diagonalization
    00:00
  • Full Example: Diagonalizing a Matrix
    00:00
  • COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**
    00:00
  • Visualizing Diagonalization & Eigenbases
    00:00
  • Similar matrices have similar properties
    00:00
  • The Similarity Relationship Represents a Change of Basis
    00:00
  • Dot Products and Length
    00:00
  • Distance, Angles, Orthogonality and Pythagoras for vectors
    00:00
  • Orthogonal bases are easy to work with!
    00:00
  • Orthogonal Decomposition Theorem Part 1: Defining the Orthogonal Compliment
    00:00
  • The geometric view on orthogonal projections
    00:00
  • Orthogonal Decomposition Theorem Part II
    00:00
  • Proving that orthogonal projections are a form of minimization
    00:00
  • Using Gram-Schmidt to orthogonalize a basis
    00:00
  • Full example: using Gram-Schmidt
    00:00
  • Least Squares Approximations
    00:00
  • Reducing the Least Squares Approximation to solving a system
    00:00

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