Linear Algebra for Data Science and Machine Learning using R

سرفصل های دوره

Vectors, Matrices, Solving Linear Equations, Factorization, Eigenvectors, Least Squares, SVD

1. Introduction

1. What you are going to learn in this course

2.1 Notes - Introduction.pdf

2. Introduction

3.1 Notes - What is Linear Algebra.pdf

3. What is Linear Algebra

4.1 Notes - Why Linear Algebra.pdf

4. Why Linear Algebra

2. Getting Started with R

1. Installing R Software

2. Installing RStudio

3. Look around RStudio Interface

4. Help & Examples Facility for R Features and Functions

5. Changing Look and Feel of RStudio

6. Some General Functions Good to Know

7. Writing R Program using RGui

8. Writing R Program using RStudio

9. Using Comments in R Scripts

3. Vectors

1.1 Notes - Scalars and Vectors.pdf

1. Scalars and Vectors

2. Vectors.html

3.1 Notes - Vectors in 2-Dimensional Space.pdf

3. Vectors in 2-Dimensional Space

4. Vectors.html

5.1 Notes - Vectors in 3-Dimensional Space.pdf

5. Vectors in 3-Dimensional Space

6.1 Notes - Vectors with n-Components.pdf

6. Vectors with n-Components

7.1 creatingvectors.zip

7. R Code - Creating Vectors

8. Creating Vectors.html

9. Practice #1.html

10.1 creatingvectorsusingsequences.zip

10. R Code - Create Vectors using Sequence Operator & Function

11. Creating Vectors using Sequence.html

12.1 accessingmodifyingvectors.zip

12. R Code - Accessing & Modifying Vectors

13. Accessing & Modifying Vectors.html

14.1 Notes - Zero and Ones Vectors.pdf

14. Zero and Ones Vectors

15. Zero and Ones Vectors.html

16.1 zeroonesvector.zip

16. R Code - Zero and Ones Vector

17. Zero and Ones Vectors.html

18.1 Quiz Solutions - Vectors.pdf

18. Quiz Solutions.html

4. Operations on Vectors

1.1 Notes - Vector Addition.pdf

1. Vector Addition

2.1 vectoraddition.zip

2. R Code - Vector Addition

3. Vector Addition.html

4.1 Notes - Vector Scalar Multiplication.pdf

4. Scalar Multiplication

5.1 scalarmultiplication.zip

5. R Code - Scalar Multiplication

6. Scalar Multiplication.html

7.1 Notes - Vector Properties.pdf

7. Vector Properties

8. Vector Properties.html

9.1 Notes - Linear Combinations of Vectors.pdf

9. Linear Combinations of Vectors

10.1 linearcombination.zip

10. R Code - Linear Combinations of Vectors

11. Linear Combination.html

12.1 Notes - Vector Transpose.pdf

12. Vector Transpose

13.1 vectortranspose.zip

13. R Code - Vector Transpose

14. Vector Transpose.html

15.1 Notes - Dot Product or Inner Product.pdf

15. Dot Product or Inner Product

16.1 dotproduct.zip

16. R Code - Dot Product

17. Dot Product.html

18.1 Notes - Outer Product.pdf

18. Outer Product

19.1 outerproduct.zip

19. R Code - Outer Product

20. Outer Product.html

21.1 Quiz Solutions - Operations on Vectors.pdf

21. Quiz Solutions.html

5. Matrices

1.1 Notes - Matrices - Context of Data Science.pdf

1. Matrices - Context of Data Science

2. Martrices.html

3.1 Notes - Dimension or Size.pdf

3. Dimension or Size

4.1 creatingmatrices.zip

4. R Code - Creating Matrices

5.1 matrixfunctions.zip

5. R Code - Matrix Functions

6. Matrices.html

7.1 namingrowscolumns.zip

7. R Code - Naming Rows and Columns of Matrix

8.1 accessingmodifyingelements.zip

8. R Code - Accessing and Modifying Elements of Matrix

9.1 appendingrowscolumns.zip

9. R Code - Appending Rows and Columns

10.1 deletingrowscolumns.zip

10. R Code - Deleting Rows and Columns of Matrix

11.1 creatingmatrixusingrbindcbind.zip

11. R Code - Creating Matrix using rbind() and cbind()

12.1 Notes - Matrix Transpose.pdf

12. Matrix Transpose

13.1 matrixtranspose.zip

13. R Code - Matrix Transpose

14. Matrix Transpose.html

15.1 Notes - Symmetric Matrix.pdf

15. Symmetric Matrix

16.1 symmetricmatrix.zip

16. R Code - Symmetric Matrix

17. Symmetric Matrices.html

18.1 Notes - Identity Matrices.pdf

18. Identity Matrices

19.1 identitymatrices.zip

19. R Code - Identity Matrices

20. Identity Matices.html

21.1 Notes - Diagonal Matrix.pdf

21. Diagonal Matrix

22.1 diagonalmatrix.zip

22. R Code - Diagonal Matrix

23. Diagonal Matrices.html

24.1 Notes - Triangular Matrix.pdf

24. Triangular Matrix

25. Triangular Matrix.html

26.1 Notes - Zero and Ones Matrix.pdf

26. Zero and Ones Matrix

27.1 zeroonesmatrix.zip

27. R Code - Zero and Ones Matrix

28. Zero and Ones Matrix.html

29.1 Quiz Solutions - Matrices.pdf

29. Quiz Solutions.html

6. Operations on Matrices

1.1 Notes - Matrix Addition.pdf

1. Matrix Addition

2.1 matrixsums.zip

2. R Code - Matrix Addition

3. Matrix Addition.html

4.1 Notes - Scalar Multiplication.pdf

4. Scalar Multiplication

5.1 scalarmultiplication.zip

5. R Code - Scalar Multiplication

6. Scalar Multiplication.html

7.1 Notes - Hadamard Product.pdf

7. Hadamard Product

8.1 hadamardproduct.zip

8. R Code - Hadamard Product

9. Hadamard Product.html

10.1 Notes - Trace of Matrix.pdf

10. Trace of Matrix

11.1 matrixtrace.zip

11. R Code - Trace of Matrix

12. Matrix Trace.html

13.1 Notes - Matrix Multiplication.pdf

13. Matrix Multiplication

14.1 matrixmultiplication.zip

14. R Code - Matrix Multiplication

15. Matrix Multiplication.html

16.1 Notes - Properties of Matrix Operations.pdf

16. Properties of Matrix Operations

17.1 Notes - Matrix Power.pdf

17. Matrix Power

18.1 matrixpower.zip

18. R Code - Matrix Power

19. Matrix Power.html

20.1 Notes - Diagonal Matrix Multiplication.pdf

20. Diagonal Matrix Multiplication

21.1 diagonalmatrixmultiplication.zip

21. R Code - Diagonal Matrix Multiplication

22.1 Quiz Solutions - Operations on Matrices.pdf

22. Quiz Solutions.html

7. Matrix Determinant and Inverse

1.1 Notes - Determinants.pdf

1. Determinants

2.1 determinants.zip

2. R Code - Determinants

3. Determinants.html

4.1 Notes - Properties of Determinants.pdf

4. Properties of Determinants

5. Determinants.html

6.1 Notes - Inverse of Matrix.pdf

6. Inverse of Matrix

7.1 matrixinverse.zip

7. R Code - Matrix Inverse

8. Matrix Inverse.html

9.1 Notes - Singular and Invertible Matrices.pdf

9. Singular and Invertible Matrices

10.1 singularmatrices.zip

10. R Code - Singular Matrices

11. Singular Matrix.html

12.1 Notes - Properties of Inverse.pdf

12. Properties of Inverse

13. Properties of Inverse.html

14.1 Quiz Solutions - Matrix Determinant and Inverse.pdf

14. Quiz Solutions.html

8. Systems of Linear Equations

1.1 Notes - System of Linear Equations.pdf

1. System of Linear Equations

2. Systems of Linear Equations.html

3.1 Notes - Types of Systems.pdf

3. Types of Systems

4.1 Notes - Matrix Notation.pdf

4. Matrix Notation

5. Matrix Notation.html

6.1 Notes - Elementary Row Operations.pdf

6. Elementary Row Operations

7.1 Notes - Gauss Elimination Method.pdf

7. Gauss Elimination Method

8. Gauss Elimination Method.html

9.1 Notes - Gauss-Jordan Elimination Method.pdf

9. Gauss-Jordan Elimination Method

10.1 gaussjordan.zip

10. R Code - Gauss Jordan Elimination Method

11. Gauss-Jordan Elimination Method.html

12.1 Quiz Solutions - System of Linear Equations.pdf

12. Quiz Solutions.html

9. Matrix Equations Ax=b

1.1 Notes - Matrix Vector Product Ax=b.pdf

1. Matrix Vector Product Ax=b

2. Matrix Vector Product.html

3.1 Notes - Systems of Equations as Linear Combinations.pdf

3. Systems of Equations as Linear Combinations

4.1 Notes - Classification of Matrix Vector Product.pdf

4. Classification of Matrix Vector Product

5.1 Notes - Solving Systems of Linear Equations using Matrix Inverse.pdf

5. Solving Systems of Linear Equations using Matrix Inverse

6.1 solveusinginverse.zip

6. R Code - Solving Systems of Linear Equations using Matrix Inverse

7. Solving Systems of Linear Equations using Matrix Inverse.html

8.1 Notes - Solving Systems of Linear Equations using Cramers Rule.pdf

8. Solving Systems of Linear Equations using Cramers Rule

9.1 cramersrule.zip

9. R Code - Solving Systems of Linear Equations using Cramers Rule

10. Solving Systems of Linear Equations using Cramers Rule.html

11.1 solve.zip

11. R Code - Solving Systems of Linear Equations using qrSolve() function

12. Solving Systems of Linear Equations.html

13.1 Quiz Solutions - Matrix Equation Ax=b.pdf

13. Quiz Solutions.html

10. Norms

1.1 Notes - Lengths and Norms.pdf

1. Lengths and Norms

2.1 Notes - L2 Norm.pdf

2. L2 Norm

3.1 l2norm.zip

3. R Code - L2 Norm

4.1 Notes - L1 Norm.pdf

4. L1 Norm

5.1 l1norm.zip

5. R Code - L1 Norm

6.1 Notes - LP Norm.pdf

6. LP Norm

7.1 lpnorm.zip

7. R Code - LP Norm

8.1 Notes - L-Infinity Norm.pdf

8. L-Infinity Norm

9.1 l-infinitynorm.zip

9. R Code - L Infinity Norm

10. Norms.html

11.1 Quiz Solutions - Norms.pdf

11. Quiz Solutions.html

11. Basis Vectors

1.1 Notes - Unit Vectors.pdf

1. Unit Vectors

2.1 unitvectors.zip

2. R Code - Unit Vectors

3.1 Notes - Standard Basis Vectors and Span.pdf

3. Standard Basis Vectors

4.1 Notes - Basis Vectors and Span.pdf

4. Basis Vectors and Span

5. Basis Vectors.html

6.1 Quiz Solutions - Basis Vectors.pdf

6. Quiz Solutions.html

12. Linear Independence

1.1 Notes - Linear Independence.pdf

1. Linear Independence - Introduction

2. Linear Independence.html

3.1 Notes - Linear Independence based on Basis Vectors.pdf

3. Linear Independence based on Basis Vectors

4.1 Notes - Linear Independence based on Determinant or Inverse.pdf

4. Linear Independence based on Determinant or Inverse

5. Linear Independence based on Determinant.html

6.1 Quiz Solutions - Linear Independence.pdf

6. Quiz Solutions.html

13. Vector Subspaces

1.1 Notes - Vector Subspaces - Introduction.pdf

1. Vector Subspaces - Introduction

2.1 Notes - Null Space.pdf

2. Null Space

3.1 nullspace.zip

3. R Code - Null Space

4.1 Notes - Null Space and Linear Independence.pdf

4. Null Space and Linear Independence

5.1 Notes - Column Space.pdf

5. Column Space

6.1 Notes - Rank and Nullity.pdf

6. Rank and Nullity

7.1 Notes - Rank-Nullity Theorem.pdf

7. Rank-Nullity Theorem

8.1 ranknullity.zip

8. R Code - Rank and Nullity

14. Matrix Factorization

1.1 Notes - Factorization.pdf

1. Factorization - Introduction

2.1 Notes - LU Factorization.pdf

2. LU Factorization

3. LU Factorization.html

4.1 Notes - Computing LU Factorization.pdf

4. Computing LU Factorization

5.1 lufactorization.zip

5. R Code - LU Factorization

6. LU Factorization.html

7.1 Quiz Solutions - Matrix Factorization.pdf

7. Quiz Solutions.html

15. Orthogonality

1.1 Notes - Orthogonal Vectors.pdf

1. Orthogonal Vectors

2.1 orthogonalvectors.zip

2. R Code - Orthogonal Vectors

3. Orthogonal Vectors.html

4.1 Notes - Orthonormal Vectors.pdf

4. Orthonormal Vectors

5.1 orthonormalvectors.zip

5. R Code - Orthonormal Vectors

6. Orthonormal Vectors.html

7.1 Notes - Orthogonal Matrix.pdf

7. Orthogonal Matrix

8.1 orthogonalmatrix.zip

8. R Code - Orthogonal Matrix

9. Orthogonal Matrix.html

10.1 Quiz Solutions - Orthogonality.pdf

10. Quiz Solutions.html

16. Eigenvalues and Eigenvectors

1.1 Notes - Eigenvalues and Eigenvectors Introduction.pdf

1. Eigenvalues and Eigenvectors - Introduction

2. Eigenvalues from Eigenvectors.html

3.1 Notes - Computing Eigenvalues from Eigenvectors.pdf

3. Computing Eigenvalues from Eigenvectors

4.1 Notes - Computing Eigenvectors from Eigenvalues.pdf

4. Computing Eigenvectors from Eigenvalues

5. Eigenvalues from Eigenvectors.html

6.1 Notes - Characteristic Equation.pdf

6. Characteristic Equation

7.1 computingeigenvalueseigenvectors.zip

7. R Code - Computing Eigenvalues and Eigenvectors

8. Computing Eigenvalues from Eigenvectors.html

9.1 Notes - Eigen Decomposition.pdf

9. Eigen Decomposition

10.1 eigendecomposition.zip

10. R Code - Eigen Decomposition

11. Eigen Decomposition.html

12.1 Notes - Diagonalization.pdf

12. Diagonalization

13.1 diagonalization.zip

13. R Code - Diagonalization

14. Diagonalization.html

15.1 Notes - Few Points - Eigenvalues and Eigenvectors.pdf

15. Few Points - Eigenvalues and Eigenvectors

16.1 Quiz Solutions - Eigenvalues and Eigenvectors.pdf

16. Quiz Solutions.html

17. Singlular Value Decomposition

1.1 Notes - Singular Value Decomposition - Introduction.pdf

1. Singular Value Decomposition - Introduction

2. Singular Value Decomposition.html

3.1 Notes - Computing Singular Value Decomposition.pdf

3. Steps for Computing SVD

4.1 svd.zip

4. R Code - Singular Value Decomposition - SVD

5. Singular Value Decomposition.html

6.1 Quiz Solutions - Singular Value Decomposition.pdf

6. Quiz Solutions.html

18. Least Squares Problem

1.1 Notes - Least Squares Problem - Introduction.pdf

1. Least Squares Problem - Introduction

2.1 Notes - Least Squares.pdf

2. Least Squares

3.1 Notes - Solving Least Squares Problems.pdf

3. Solving Least Squares

4.1 leastsquares.zip

4. R Code - Solving Least Squares

19. Moore-Penrose Pseudoinverse

1.1 Notes - Moore-Penrose Pseudoinverse.pdf

1. Moore-Penrose Pseudoinverse

2.1 moorepenrose.zip

2. R Code - Moore Penrose Pseudoinverse

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