Linear Algebra for Beginners: Open Doors to Great Careers

Watch Linear Algebra for Beginners: Open Doors to Great Careers

  • 2015
  • 1 Season

Linear Algebra for Beginners: Open Doors to Great Careers is a comprehensive three-part series created by Richard Han that offers an accessible introduction to the mathematical principles of linear algebra. From machine learning and data analysis to economics and engineering, linear algebra is a fundamental discipline that underpins many modern fields of study. With Han's engaging and easy-to-follow teaching style, viewers will gain a solid understanding of the concepts and applications of linear algebra and how it can lead to exciting career paths.

The first episode of the series covers the basics of linear algebra, starting with the definition of vectors and matrices. Han uses real-world examples to illustrate how these mathematical concepts can be applied in fields such as physics, finance, and image processing. He also delves into the properties of vectors and matrices, including addition, scalar multiplication, and matrix multiplication. By the end of the episode, viewers will have a solid foundation in the language of linear algebra and the tools to tackle more complex topics in later episodes.

The second episode focuses on linear transformations and their properties. Han starts by explaining what a linear transformation is and why it is important in various fields. He then dives into matrices as linear transformations, discussing concepts like range, null space, and invertibility. Han also covers eigenvectors and eigenvalues, two fundamental concepts in linear algebra that are essential to many applications. By the end of the episode, viewers will have a solid understanding of the properties of linear transformations and how they can be used to solve real-world problems.

The final episode of the series covers advanced topics in linear algebra, including applications to machine learning and data analysis. Han introduces the concept of a vector space and the importance of basis vectors, which are used to define a coordinate system within a space. He then discusses linear regression and principal component analysis, two common techniques used in machine learning and data analysis. Han also touches on topics like singular value decomposition and eigenfaces, which are used in fields such as computer vision and image recognition.

Throughout the series, Han reinforces key concepts with clear and concise explanations, supplemented by helpful visual aids and real-world examples. He also provides quizzes and exercises to help viewers test their understanding and apply what they have learned. Perhaps most importantly, Han emphasizes the importance of linear algebra in many exciting career fields, including computer science, finance, and data analysis. With his encouragement and guidance, viewers will be inspired to unlock the full potential of linear algebra and open doors to great career opportunities.

Overall, Linear Algebra for Beginners: Open Doors to Great Careers is an excellent resource for anyone looking to learn about linear algebra or prepare for a career in a related field. With Richard Han's expertise and engaging teaching style, viewers will acquire a solid foundation in the principles and applications of linear algebra and be well-prepared to tackle more advanced topics in the field.

Linear Algebra for Beginners: Open Doors to Great Careers is a series that ran for 1 seasons (43 episodes) between January 1, 2015 and on Richard Han

Linear Algebra for Beginners: Open Doors to Great Careers
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Seasons
Examples of Finding Transition Matrices
44. Examples of Finding Transition Matrices
 
Students will learn how to find transition matrices from one basis to another.
Change of Basis
43. Change of Basis
 
Students will learn what change of basis means and what a transition matrix from one basis to another is.
Coordinates
42. Coordinates
 
Students will learn what the coordinates of a vector relative to a basis are and what the coordinate matrix of a vector relative to a basis is.
Dimension
41. Dimension
 
Students will learn how to find the dimension of a vector space.
Basis
40. Basis
 
Students will learn how to show that a subset of a vector space is a basis for the vector space.
Determining Linear Independence or Dependence
39. Determining Linear Independence or Dependence
 
Students will learn how to determine if a subset of a vector space is linearly independent or dependent.
Linear Independence
38. Linear Independence
 
Students will learn what it means for a subset of a vector space to be linearly independent.
Span of a Subset of a Vector Space
37. Span of a Subset of a Vector Space
 
Students will learn what the span of a subset of a vector space is.
Span
36. Span
 
Students will learn how to show that a subset of a vector space spans the vector space and how to show that a subset of a vector space does not span the vector space.
Subsets that are Not Subspaces: Additional Example
35. Subsets that are Not Subspaces: Additional Example
 
An additional example of a subset that is not a subspace is discussed.
Subsets that are Not Subspaces
34. Subsets that are Not Subspaces
 
An example of a subset of R2 that is not a subspace of R2 is discussed. Students will learn how to show that a subset of a vector space is not a subspace of that vector space.
Additional Example of Subspace
33. Additional Example of Subspace
 
An example of a subspace of M(2,2), the set of all 2 by 2 matrices, is provided.
Definition of Trivial and Nontrivial Subspace
32. Definition of Trivial and Nontrivial Subspace
 
The definition of a trivial subspace and of a nontrivial subspace are provided.
Subspace Definition and Subspace Properties
31. Subspace Definition and Subspace Properties
 
The definition of a subspace is provided, and the three subspace properties are outlined. An example of a proof showing that a subset of R2 is a subspace is demonstrated. Students will learn how to show that a subset of a vector space is a subspace.
Examples of Sets that are Not Vector Spaces
30. Examples of Sets that are Not Vector Spaces
 
Examples of sets that are not vector spaces are discussed. Students will learn how to detect when a set is a not a vector space.
Vector Space: Additional Example Continued
29. Vector Space: Additional Example Continued
 
The proof of the first five properties of a vector space applied to P2 is continued.
Vector Space: Additional Example
28. Vector Space: Additional Example
 
An additional example of a vector space is provided.
Vector Space Example: Continued
27. Vector Space Example: Continued
 
The proof of the claim that R2 is a vector space is continued.
Vector Space Example
26. Vector Space Example
 
A proof is given to show that R2 is a vector space. Students will learn how to prove a set is a vector space.
Vector Space Definition
25. Vector Space Definition
 
The definition of vector space is explained. Students will learn what a vector space is.
Determinant of the Transpose of a Matrix
24. Determinant of the Transpose of a Matrix
 
The determinant of the transpose of a matrix is discussed. Students will learn how to find the determinant of the transpose of a matrix.
Determinants and Invertibility
23. Determinants and Invertibility
 
The relationship between determinants and invertibility is explained. Students will be able to determine when a matrix is invertible by examining the determinant.
Determinant of a Product of Matrices and of a Scalar Multiple of a Matrix
22. Determinant of a Product of Matrices and of a Scalar Multiple of a Matrix
 
The determinant of a product of two matrices and the determinant of a scalar multiple of a matrix are discussed. Students will be able to find the determinant of a product of matrices and the determinant of a scalar multiple of a matrix.
Cofactor Expansion: Additional Examples
21. Cofactor Expansion: Additional Examples
 
Additional examples of cofactor expansion are provided.
Cofactor Expansion
20. Cofactor Expansion
 
The process of Cofactor Expansion is explained. Students will learn how to apply cofactor expansion to find the determinant of a 3 by 3 matrix.
Determinant of a 2 by 2 Matrix
19. Determinant of a 2 by 2 Matrix
 
The formula for the determinant of a 2 by 2 matrix is introduced. Students will learn how to find the determinant of a 2 by 2 matrix.
Gauss-Jordan Elimination: Additional Example
18. Gauss-Jordan Elimination: Additional Example
 
An additional example of Gauss-Jordan Elimination is provided.
Gauss-Jordan Elimination
17. Gauss-Jordan Elimination
 
The process of Gauss-Jordan Elimination is explained. Students will learn how to find the inverse of a matrix using Gauss-Jordan Elimination.
Inverse Matrix
16. Inverse Matrix
 
The definition of inverse matrix is introduced and the formula for the inverse of a 2 by 2 matrix is given. Students will learn what an inverse matrix is.
Transpose of a Matrix
15. Transpose of a Matrix
 
The definition of transpose of a matrix is provided, and properties of the transpose are introduced. Students will learn how to find the transpose of a matrix and how to apply properties of transposes.
Identities, Additive Inverses, and Multiplicative Associativity and Distributivity
14. Identities, Additive Inverses, and Multiplicative Associativity and Distributivity
 
The properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity are introduced. Students will learn how to apply properties of additive and multiplicative identities, additive inverses, and multiplicative associativity and distributivity.
Commutativity, Associativity, and Distributivity
13. Commutativity, Associativity, and Distributivity
 
The properties of additive commutativity and associativity are introduced. The distributivity properties are also introduced. Students will learn how to apply the additive commutativity, additive associativity, and distributivity properties.
Multiplication
12. Multiplication
 
The matrix operation of multiplication is introduced. Students will learn how to multiply two matrices.
Addition and Scalar Multiplication
11. Addition and Scalar Multiplication
 
The matrix operations of addition and scalar multiplication are introduced. Students will learn how to add two matrices and how to multiply a matrix by a scalar.
Linear Independence: Example 2
10. Linear Independence: Example 2
 
A second example of determining linear independence is provided. Students will learn how to determine when a set of vectors is linearly independent.
Linear Independence: Example 1
9. Linear Independence: Example 1
 
An example of determining linear independence is provided. Students will learn how to determine when a set of vectors is linearly independent.
Vector Equations and the Matrix Equation Ax=b
7. Vector Equations and the Matrix Equation Ax=b
 
In this lecture, the notion of span is introduced and it is shown how a system of equations can be rewritten as a matrix equation.
Vector Operations and Linear Combinations
6. Vector Operations and Linear Combinations
 
The vector operations of addition, scalar multiplication, and matrix multiplication are introduced and the definition of linear combination is provided. Students will learn how to add two vectors, multiply a vector by a scalar, and multiply a vector by a matrix. The student will understand what linear combinations are and what weights are.
Elementary Row Operations: Additional Example
5. Elementary Row Operations: Additional Example
 
An additional example of applying row operations is provided.
Elementary Row Operations
4. Elementary Row Operations
 
The augmented matrix is introduced and the elementary row operations are defined. Students will learn how to apply elementary row operations to an augmented matrix.
Gaussian Elimination and Row Echelon Form
3. Gaussian Elimination and Row Echelon Form
 
In this lecture, the row echelon form is introduced and many examples of Gaussian elimination are worked out. Students will learn how to apply Gaussian elimination to solve systems of linear equations. Students will also see the three different cases in regard to solutions to systems of equations.
Gaussian Elimination
2. Gaussian Elimination
 
In this lecture, we discuss Gaussian Elimination and examples of solving a system of linear equations. Students will learn about the three moves in Gaussian elimination.
Introduction Lecture
1. Introduction Lecture
 
An introduction to the course is provided.
Description
Where to Watch Linear Algebra for Beginners: Open Doors to Great Careers
Linear Algebra for Beginners: Open Doors to Great Careers is available for streaming on the Richard Han website, both individual episodes and full seasons. You can also watch Linear Algebra for Beginners: Open Doors to Great Careers on demand at Amazon.
  • Premiere Date
    January 1, 2015