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Learning Linear Algebra Through Programming

Intermediate 4.2

12 months 30 days

$348.00 $278.00

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4.2
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A linear algebra course specially designed for programmers, with a new course design model, cooperates with programming explanations, rejects boring example explanations, but explains the ins and outs of each knowledge point clearly and completely learns the knowledge system in the field of linear algebra.

Welcome to "Linear Algebra for Programmers"

  • Guide to "Linear Algebra Course Designed for Programmers"
    27:27
  • More supplementary instructions on course study
    20:54
  • Linear Algebra and Machine Learning
    27:22
  • Construction of course use environment
    16:08

It all starts with vectors

  • What is a vector.
    25:12
  • More terms and representations for vectors
    15:56
  • Implement our own vector
    13:17
  • Two basic operations on vectors.
    15:40
  • Implement basic vector operations.
    18:49
  • The nature of basic vector operations and the establishment of a mathematical building.
    23:46
  • Zero vector.
    26:29
  • Implement zero vector
    16:12
  • It all starts with vectors
    22:23

Advanced topics of vectors

  • Normalization and unit vector.
    17:51
  • Implement vector normalization
    21:09
  • Point product and geometric meaning of vector.
    13:52
  • Intuitive understanding of vector dot product
    28:55
  • Implement dot multiplication of vectors
    10:43
  • Application of vector dot product.
    18:16
  • Basic use of vectors in Numpy
    19:41

A matrix is not just m*n numbers

  • What is a matrix
    17:23
  • Implement our own matrix class
    10:06
  • Basic operations and basic properties of matrices
    19:26
  • Implement basic operations of matrices
    10:03
  • Think of a matrix as a description of the system
    23:17
  • Multiplication of matrices and vectors and treating matrices as a function of vectors
    20:31
  • Matrix and multiplication of matrices
    27:07
  • Implement multiplication of matrices
    27:41
  • Properties of matrix multiplication and power of matrix
    14:16
  • of a transpose of a
    14:27
  • Implement transpose of matrices and matrices in Numpy
    27:46

Applications of matrices and more advanced topics related to matrices

  • More transformation matrices
    14:21
  • Matrix rotation transformation and matrix application in graphics
    17:59
  • Realizing the application of matrix transformation in graphics
    12:52
  • From scaling transformation to identity matrix
    14:46
  • matrix inversion
    11:57
  • Implement the inverse of the identity matrix and the matrix in numpy
    12:40
  • Properties of the inverse of a matrix
    13:26
  • Key perspective on matrices: Using matrices to represent space
    17:26
  • Summary: Four important perspectives on matrices
    10:39

linear system

  • Linear System and Elimination Method
    10:43
  • Gauss elimination method
    29:54
  • Gauss-Jordan elimination
    13:33
  • Implement Gauss-Jordan elimination method
    19:31
  • The simplest form of rows and the structure of solutions to linear equations
    11:26
  • Intuitive understanding of the structure of solutions to linear equations
    17:09
  • More general Gauss-Jordan elimination method
    28:12
  • Implement a more general Gauss-Jordan elimination method
    21:49
  • homogeneous linear equations
    10:34

Elementary matrices and invertibility of matrices

  • Linear systems and the inverse of matrices
    27:40
  • Implement the inverse of the solution matrix
    17:27
  • elementary matrix
    18:05
  • From elementary matrices to the inverse of matrices
    20:57
  • Why is the inverse of the matrix so important?
    26:29
  • LU decomposition of matrix
    14:50
  • Implement LU decomposition of matrices
    12:53
  • LU factorization of non-square matrices, LDU factorization and PLU factorization of matrices
    26:51
  • PLUP factorization of matrices and looking back at multiplication of matrices
    27:50

Linear dependence, linear independence and generation space

  • linear combination
    21:34
  • Linear dependence and linear independence
    14:34
  • The inverse sum of a matrix is linearly dependent and linearly independent
    18:29
  • Intuitive understanding of linear dependence and linear independence
    11:14
  • generate spatial
    15:01
  • basis of space
    29:55
  • More properties of bases of spaces
    27:03
  • Summary of this chapter: Forming your own knowledge map
    27:11

Vector space, dimensions, and four major subspaces

  • Space, vector space and Euclidean space
    20:27
  • generalized vector space
    25:20
  • subspace
    25:16
  • Intuitive understanding of subspaces of Euclidean space
    12:23
  • dimension
    21:37
  • Row space and row rank of matrix
    14:43
  • column space
    27:43
  • The rank of a matrix and the inverse of a matrix
    10:41
  • rank of realization matrix
    20:38
  • Zero space and three perspectives on zero space
    23:42
  • Zero Space and Rank-Neutralization Degree Theorem
    14:47
  • Left null space, four major subspaces and reasons for studying subspaces
    25:48

orthogonality, orthonormal matrices and projections

  • Orthogonal basis and orthonormal basis
    19:12
  • one-dimensional projection
    10:16
  • High-dimensional projections and Gram-Schmidt processes
    17:01
  • Implementing the Gram-Schmidt process
    28:08
  • Properties of orthonormal bases
    25:08
  • QR decomposition of matrix
    12:53
  • Implement QR decomposition of matrices
    28:47
  • This chapter summarizes and more projection-related topics
    22:37

Coordinate transformation and linear transformation

  • Basis and coordinate system of space
    17:39
  • Conversion of other coordinate systems to standard coordinate systems
    27:14
  • arbitrary coordinate system conversion
    28:05
  • linear transformation
    19:51
  • More topics related to coordinate transformation and linear transformation
    23:25

determinant

  • What is a determinant
    16:30
  • Four basic properties of determinant
    24:41
  • Determinant and the inverse of matrix
    13:58
  • Algorithm for calculating determinant
    27:47
  • Elementary matrices and determinants
    29:54
  • A row form is a column form!
    24:17
  • Algebra expression of flashy determinant
    27:56

eigenvalue and eigenvector

  • What are eigenvalues and eigenvectors
    10:29
  • Related concepts of eigenvalues and eigenvectors
    29:58
  • Properties of Eigenvalues and Eigenvectors
    12:16
  • Intuitive understanding of eigenvalues and eigenvectors
    16:29
  • Eigenvalues of "not simple"
    20:30
  • Solving eigenvalues and eigenvectors in practicing numpy
    15:02
  • Matrix similarities and the important meaning behind them
    17:10
  • matrix diagonalization
    24:03
  • Achieve your own matrix diagonalization
    15:59
  • Application of matrix diagonalization: Solving the power sum of matrices for dynamic systems
    11:56

Symmetric matrices and SVD decomposition of matrices

  • Perfect symmetric matrix
    14:33
  • orthogonal diagonalization
    26:14
  • What is a singular value
    26:05
  • Geometric meaning of singular values
    24:10
  • SVD decomposition of singular values
    16:40
  • Practice SVD decomposition in scipy
    22:12
  • Application of SVD decomposition
    23:20

For the broader world of linear algebra, come on everyone!

  • For the broader world of linear algebra, come on everyone!
    19:09
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liuyubobobo
liuyubobobo
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