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The sequel to the course Linear Algebra for Beginners: Open Doors to Great Careers.

Would you like to learn a mathematics subject that is crucial for many highdemand lucrative career fields such as:
If you're looking to gain a solid foundation in Linear Algebra, allowing you to study on your own schedule at a fraction of the cost it would take at a traditional university, to further your career goals, this online course is for you. If you're a working professional needing a refresher on linear algebra or a complete beginner who needs to learn Linear Algebra for the first time, this online course is for you.
Why you should take this online course: You need to refresh your knowledge of linear algebra for your career to earn a higher salary. You need to learn linear algebra because it is a required mathematical subject for your chosen career field such as computer science or electrical engineering. You intend to pursue a masters degree or PhD, and linear algebra is a required or recommended subject.
Why you should choose this instructor: I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International.
In this course, I cover the core concepts such as:
After taking this course, you will feel CAREFREE AND CONFIDENT. I will break it all down into bitesized nobrainer chunks. I explain each definition and go through each example STEP BY STEP so that you understand each topic clearly. I will also be AVAILABLE TO ANSWER ANY QUESTIONS you might have on the lecture material or any other questions you are struggling with.
Practice problems are provided for you, and detailed solutions are also provided to check your understanding.
30 day full refund if not satisfied.
Grab a cup of coffee and start listening to the first lecture. I, and your peers, are here to help. We're waiting for your insights and questions! Enroll now!
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Section 1: Introduction  

Lecture 1 
Introduction
Preview

04:00  
Section 2: Inner Product Spaces  
Lecture 2  17:01  
The notion of a norm is introduced. Students will learn how to find the norm of a vector and how to find the unit vector in the direction of a given vector. 

Lecture 3  09:20  
The notion of the distance between two vectors is introduced. Students will learn how to find the distance between two vectors. 

Lecture 4  19:57  
The notion of the angle between two vectors is introduced. The notions of dot product and orthogonality are introduced as well. Students will learn how to find the angle between two vectors and how to find the dot product of two vectors. 

Lecture 5  1 page  
Practice problems for norms and dot product for Rn. 

Lecture 6  2 pages  
Solutions to Problem Set: Norms and Dot Product for Rn 

Lecture 7  11:08  
The definitions of inner product and of inner product spaces are provided. 

Lecture 8  12:34  
Students will learn about some examples of inner product and of inner product spaces. 

Lecture 9  18:56  
The definitions of norm, distance, and angle between two vectors in an inner product space are provided. 

Lecture 10  08:06  
An additional example of norm, distance, and angle for inner product spaces is provided. 

Lecture 11  12:51  
Students will learn how to find the orthogonal projection of one vector onto another vector. 

Lecture 12  2 pages  
Practice problems for inner product spaces. 

Lecture 13  2 pages  
Solutions to Problem Set: Inner Product Spaces 

Lecture 14  10:55  
The definitions of orthogonal basis and of orthonormal basis are provided. 

Lecture 15  15:15  
Students will learn how to find the coordinates of a vector relative to a given orthonormal basis. 

Lecture 16  08:09  
Students will learn what the GramSchmidt process is. 

Lecture 17  12:45  
Students will learn how to apply the GramSchmidt process. 

Lecture 18  15:42  
An additional example of applying the GramSchmidt process is provided. 

Lecture 19  1 page  
Practice problems for orthonormal bases. 

Lecture 20  4 pages  
Solutions to Problem Set: Orthonormal Bases 

Lecture 21  09:12  
The leastsquares problem is introduced. 

Lecture 22  13:59  
Students will learn how to solve leastsquares problems. 

Lecture 23  1 page  
Practice problems for least squares problems. 

Lecture 24  5 pages  
Solutions to Problem Set: Least Squares Problems 

Section 3: Linear Transformations  
Lecture 25  14:09  
The definition of linear transformation is provided. 

Lecture 26  06:55  
Students will learn about linear transformations represented by matrices. 

Lecture 27  1 page  
Practice problems for linear transformations. 

Lecture 28  2 pages  
Solutions to Problem Set: Linear Transformations 

Lecture 29  13:05  
The definition of the kernel of a linear transformation is provided. Students will learn how to find the kernel of a linear transformation. 

Lecture 30  08:23  
Students will learn how to find a basis for the kernel of a linear transformation. 

Lecture 31  05:41  
The definition of the range of a linear transformation is provided. 

Lecture 32  04:58  
Students will learn how to find a basis for the range of a linear transformation. 

Lecture 33  09:47  
The definitions of rank and nullity of a linear transformation are provided. Students will learn how the rank and nullity of a linear transformation are related. 

Lecture 34  14:34  
The definitions of the onetoone and onto properties are provided. Students will learn how to show that a given linear transformation is onetoone and how to show that a given linear transformation is onto. 

Lecture 35  03:52  
The definition of isomorphism is provided. 

Lecture 36  2 pages  
Practice problems for the kernel and range of a linear transformation. 

Lecture 37  7 pages  
Solutions to Problem Set: The Kernel and Range of a Linear Transformation 

Lecture 38  14:52  
Students will learn how to find the standard matrix for a linear transformation and how to find the matrix of a linear transformation relative to the bases B and B'. 

Lecture 39  17:11  
Students will learn how to find the matrix of a linear transformation relative to the bases B and B'. 

Lecture 40  12:25  
Additional examples of finding the matrix of T relative to the bases B and B' are provided. 

Lecture 41  1 page  
Practice problems for matrix representation of linear transformations. 

Lecture 42  4 pages  
Solutions to Problem Set: Matrix Representation of Linear Transformations 

Lecture 43  08:04  
Students will learn about reflections and rotations in the plane. 

Lecture 44  05:48  
Students will learn how to apply compositions of linear transformations. 

Lecture 45  15:33  
Students will learn how to apply rotations in 3dimensional space. 

Lecture 46  1 page  
Practice problems for applications of linear transformations. 

Lecture 47  2 pages  
Solutions to Problem Set: Applications of Linear Transformations 

Lecture 48 
Review Request

1 page  
Section 4: Eigenvalues and Eigenvectors  
Lecture 49  14:37  
The definitions of eigenvalue, eigenvector, and eigenspace are provided. Students will learn the geometric interpretation of eigenvalues and eigenvectors. 

Lecture 50  07:15  
Students will learn how to find the eigenvalues and eigenvectors of a matrix. 

Lecture 51  10:13  
An example of finding eigenvalues and eigenvectors of a matrix is provided. 

Lecture 52  14:36  
An additional example of finding eigenvalues and eigenvectors is provided. The notion of multiplicity of an eigenvalue is also introduced. 

Lecture 53  1 page  
Practice problems for eigenvalues and eigenvectors. 

Lecture 54  4 pages  
Solutions to Problem Set: Eigenvalues and Eigenvectors 

Lecture 55  13:01  
The notion of diagonalizability is introduced. 

Lecture 56  15:30  
Students will learn about a necessary and sufficient condition for diagonalizability. 

Lecture 57  05:15  
Students will learn about a necessary and sufficient condition for diagonalizability. 

Lecture 58  04:43  
Students will learn how to diagonalize a matrix. 

Lecture 59  1 page  
Practice problems for diagonalization. 

Lecture 60  5 pages  
Solutions to Problem Set: Diagonalization 

Lecture 61  14:19  
Students will learn how to apply diagonalization to solving a system of linear differential equations. 

Lecture 62  13:38  
An example of solving a system of linear differential equations is provided. 

Lecture 63  1 page  
Practice problems for applications to differential equations. 

Lecture 64  3 pages  
Solutions to Problem Set: Applications to Differential Equations 

Section 5: Symmetric Matrices and Orthogonal Diagonalization  
Lecture 65  03:17  
Students will learn about the properties of symmetric matrices. 

Lecture 66  17:52  
An example of verifying the properties of symmetric matrices is provided. 

Lecture 67  19:54  
The definition of orthogonal diagonalization is provided. Students will learn how to orthogonally diagonalize a matrix. 

Lecture 68  06:45  
The steps of orthogonal diagonalization are summarized. 

Lecture 69  03:31  
The properties of symmetric matrices are summarized in the Spectral Theorem for Symmetric Matrices. 

Lecture 70  1 page  
Practice problems for symmetric matrices and orthogonal diagonalization. 

Lecture 71  5 pages  
Solutions to Problem Set: Symmetric Matrices and Orthogonal Diagonalization 

Lecture 72  13:07  
Quadratic forms are introduced, and several examples are provided. 

Lecture 73  06:30  
Students will learn how to apply orthogonal diagonalization to eliminating crossproduct terms in quadratic forms. 

Lecture 74  13:42  
An example of eliminating crossproduct terms in a quadratic form is provided. 

Lecture 75  05:38  
Students will learn about the Principal Axes Theorem. 

Lecture 76  1 page  
Practice problems for quadratic forms. 

Lecture 77  2 pages  
Solutions to Problem Set: Quadratic Forms 

Lecture 78  08:44  
Students will learn what a singular value decomposition of a matrix is. 

Lecture 79  14:05  
An example of finding a singular value decomposition of a matrix is provided. Students will learn how to find a singular value decomposition of a matrix. 

Lecture 80  13:50  
An example of finding a singular value decomposition of a matrix is provided. Students will learn how to find a singular value decomposition of a matrix. 

Lecture 81  1 page  
Practice problems for singular value decomposition. 

Lecture 82  6 pages  
Solutions to Problem Set: Singular Value Decomposition 

Section 6: Application of SVD to Statistics: Principal Component Analysis  
Lecture 83  09:35  
Students will learn what meandeviation form is and what a covariance matrix is. 

Lecture 84  09:21  
Students will see an illustration of meandeviation form and covariance matrix. Students will also learn what variance is. 

Lecture 85  10:16  
The notion of principal component is introduced. Students will learn how singular value decomposition is useful for finding principal components. 

Section 7: Conclusion  
Lecture 86 
Concluding Letter

1 page  
Lecture 87 
Bonus Lecture

2 pages 
Hi there! My name is Richard Han. I earned my PhD in Mathematics from the University of California, Riverside. I have extensive teaching experience: 6 years as a teaching assistant at University of California, Riverside, over two years as a faculty member at Western Governors University, #1 in secondary education by the National Council on Teacher Quality, and as a faculty member at Trident University International. My expertise includes calculus and linear algebra. I am an instructor on Udemy for the courses Philosophy of Language: Solidify Critical Thinking Skills and Linear Algebra for Beginners: Open Doors to Great Careers.