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Linear Algebra for Beginners: Open Doors to Great Careers 2

Name: Linear Algebra for Beginners: Open Doors to Great Careers 2
Rating: 4.4 (85 reviews)

Learn the core topics of Linear Algebra to open doors to Computer Science, Data Science, Actuarial Science, and more!

Created byRichard Han

Last updated 5/2018

English

What you'll learn

Refresh your math knowledge.
Gain a firm foundation in Linear Algebra for furthering your career.
Learn one of the mathematical subjects crucial for Computer Science.
Learn one of the mathematical subjects crucial for engineering, computer science, physics, economics, computer animation, and cryptography among many others.
Learn one of the mathematical subjects needed for Data Science.
Learn a mathematical subject useful in becoming a Quant on Wall Street.

Course content

7 sections • 87 lectures • 10h 24m total length

Introduction4:00

Norms for Rn17:01
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.
Distance Between Vectors in Rn9:20
The notion of the distance between two vectors is introduced.

Students will learn how to find the distance between two vectors.
Angle Between Vectors in Rn19:57
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.
Problem Set: Norms and Dot Product for Rn1:00
Practice problems for norms and dot product for Rn.
Solutions to Problem Set: Norms and Dot Product for Rn2:00
Solutions to Problem Set: Norms and Dot Product for Rn
Inner Product Spaces11:08
The definitions of inner product and of inner product spaces are provided.
Examples of Inner Product12:34
Students will learn about some examples of inner product and of inner product spaces.
Norm, Distance, and Angle for Inner Product Spaces18:56
The definitions of norm, distance, and angle between two vectors in an inner product space are provided.
Additional Example of Norm, Distance, and Angle for Inner Product Spaces8:06
An additional example of norm, distance, and angle for inner product spaces is provided.
Orthogonal Projection12:51
Students will learn how to find the orthogonal projection of one vector onto another vector.
Problem Set: Inner Product Spaces2:00
Practice problems for inner product spaces.
Solutions to Problem Set: Inner Product Spaces2:00
Solutions to Problem Set: Inner Product Spaces
Orthonormal Bases10:55
The definitions of orthogonal basis and of orthonormal basis are provided.
Coordinates Relative to an Orthonormal Basis15:15
Students will learn how to find the coordinates of a vector relative to a given orthonormal basis.
Gram-Schmidt Process8:09
Students will learn what the Gram-Schmidt process is.
Example of Gram-Schmidt Process12:45
Students will learn how to apply the Gram-Schmidt process.
Additional Example of the Gram-Schmidt Process15:42
An additional example of applying the Gram-Schmidt process is provided.
Problem Set: Orthonormal Bases1:00
Practice problems for orthonormal bases.
Solutions to Problem Set: Orthonormal Bases4:00
Solutions to Problem Set: Orthonormal Bases
Least-Squares Problems9:12
The least-squares problem is introduced.
Example of Least-Squares Problem13:59
Students will learn how to solve least-squares problems.
Problem Set: Least Squares Problems1:00
Practice problems for least squares problems.
Solutions to Problem Set: Least Squares Problems5:00
Solutions to Problem Set: Least Squares Problems

Linear Transformations14:09
The definition of linear transformation is provided.
Linear Transformations Represented by Matrices6:55
Students will learn about linear transformations represented by matrices.
Problem Set: Linear Transformations1:00
Practice problems for linear transformations.
Solutions to Problem Set: Linear Transformations2:00
Solutions to Problem Set: Linear Transformations
Kernel of a Linear Transformation13:05
The definition of the kernel of a linear transformation is provided.

Students will learn how to find the kernel of a linear transformation.
The Kernel of T as a Subspace of V8:23
Students will learn how to find a basis for the kernel of a linear transformation.
The Range of a Linear Transformation5:41
The definition of the range of a linear transformation is provided.
Finding a Basis for Range(T)4:58
Students will learn how to find a basis for the range of a linear transformation.
Rank and Nullity of a Linear Transformation9:47
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.
One-to-one and Onto Properties14:34
The definitions of the one-to-one and onto properties are provided.

Students will learn how to show that a given linear transformation is one-to-one and how to show that a given linear transformation is onto.
Isomorphisms3:52
The definition of isomorphism is provided.
Problem Set: The Kernel and Range of a Linear Transformation2:00
Practice problems for the kernel and range of a linear transformation.
Solutions to Problem Set: The Kernel and Range of a Linear Transformation7:00
Solutions to Problem Set: The Kernel and Range of a Linear Transformation
Matrix Representation of Linear Transformations14:52
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'.
Example of the Matrix of T Relative to the Bases B and B'17:11
Students will learn how to find the matrix of a linear transformation relative to the bases B and B'.
Additional Example of the Matrix of T Relative to the Bases B and B'12:25
Additional examples of finding the matrix of T relative to the bases B and B' are provided.
Problem Set: Matrix Representation of Linear Transformations1:00
Practice problems for matrix representation of linear transformations.
Solutions to Problem Set: Matrix Representation of Linear Transformations4:00
Solutions to Problem Set: Matrix Representation of Linear Transformations
Applications of Linear Transformations8:04
Students will learn about reflections and rotations in the plane.
Composition of Linear Transformations5:48
Students will learn how to apply compositions of linear transformations.
Application to Computer Graphics15:33
Students will learn how to apply rotations in 3-dimensional space.
Problem Set: Applications of Linear Transformations1:00
Practice problems for applications of linear transformations.
Solutions to Problem Set: Applications of Linear Transformations2:00
Solutions to Problem Set: Applications of Linear Transformations
Review Request1:00

Eigenvalues and Eigenvectors14:37
The definitions of eigenvalue, eigenvector, and eigenspace are provided.

Students will learn the geometric interpretation of eigenvalues and eigenvectors.
Finding Eigenvalues and Eigenvectors of a Matrix7:15
Students will learn how to find the eigenvalues and eigenvectors of a matrix.
Example of Finding Eigenvalues and Eigenvectors10:13
An example of finding eigenvalues and eigenvectors of a matrix is provided.
Additional Example of Finding Eigenvalues and Eigenvectors14:36
An additional example of finding eigenvalues and eigenvectors is provided. The notion of multiplicity of an eigenvalue is also introduced.
Problem Set: Eigenvalues and Eigenvectors1:00
Practice problems for eigenvalues and eigenvectors.
Solutions to Problem Set: Eigenvalues and Eigenvectors4:00
Solutions to Problem Set: Eigenvalues and Eigenvectors
Diagonalization13:01
The notion of diagonalizability is introduced.
A Necessary and Sufficient Condition for Diagonalizability15:30
Students will learn about a necessary and sufficient condition for diagonalizability.
A Necessary and Sufficient Condition for Diagonalizability (Continued)5:15
Students will learn about a necessary and sufficient condition for diagonalizability.
Diagonalizing a Matrix4:43
Students will learn how to diagonalize a matrix.
Problem Set: Diagonalization1:00
Practice problems for diagonalization.
Solutions to Problem Set: Diagonalization5:00
Solutions to Problem Set: Diagonalization
Applications to Differential Equations14:19
Students will learn how to apply diagonalization to solving a system of linear differential equations.
Example of Solving a System of Linear Differential Equations13:38
An example of solving a system of linear differential equations is provided.
Problem Set: Applications to Differential Equations1:00
Practice problems for applications to differential equations.
Solutions to Problem Set: Applications to Differential Equations3:00
Solutions to Problem Set: Applications to Differential Equations

Symmetric Matrices3:17
Students will learn about the properties of symmetric matrices.
Example of Verifying Properties of Symmetric Matrices17:52
An example of verifying the properties of symmetric matrices is provided.
Orthogonal Diagonalization19:54
The definition of orthogonal diagonalization is provided.

Students will learn how to orthogonally diagonalize a matrix.
Summary of Orthogonal Diagonalization6:45
The steps of orthogonal diagonalization are summarized.
The Spectral Theorem for Symmetric Matrices3:31
The properties of symmetric matrices are summarized in the Spectral Theorem for Symmetric Matrices.
Problem Set: Symmetric Matrices and Orthogonal Diagonalization1:00
Practice problems for symmetric matrices and orthogonal diagonalization.
Solutions to Problem Set: Symmetric Matrices and Orthogonal Diagonalization5:00
Solutions to Problem Set: Symmetric Matrices and Orthogonal Diagonalization
Quadratic Forms13:07
Quadratic forms are introduced, and several examples are provided.
Eliminating Cross-product Terms6:30
Students will learn how to apply orthogonal diagonalization to eliminating cross-product terms in quadratic forms.
Example of Eliminating Cross-product Terms13:42
An example of eliminating cross-product terms in a quadratic form is provided.
The Principal Axes Theorem5:38
Students will learn about the Principal Axes Theorem.
Problem Set: Quadratic Forms1:00
Practice problems for quadratic forms.
Solutions to Problem Set: Quadratic Forms2:00
Solutions to Problem Set: Quadratic Forms
Singular Value Decomposition8:44
Students will learn what a singular value decomposition of a matrix is.
Example of Finding a Singular Value Decomposition of a Matrix14:05
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.
Example of Finding a Singular Value Decomposition of a Matrix (Continued)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.
Problem Set: Singular Value Decomposition1:00
Practice problems for singular value decomposition.
Solutions to Problem Set: Singular Value Decomposition6:00
Solutions to Problem Set: Singular Value Decomposition

Mean-Deviation Form and Covariance Matrix9:35
Students will learn what mean-deviation form is and what a covariance matrix is.
Illustration of Mean-Deviation Form and Covariance Matrix9:21
Students will see an illustration of mean-deviation form and covariance matrix. Students will also learn what variance is.
Principal Component Analysis10:16
The notion of principal component is introduced.

Students will learn how singular value decomposition is useful for finding principal components.

Requirements

The Udemy Course "Linear Algebra for Beginners; Open Doors to Great Careers"

Description

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

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Would you like to learn a mathematics subject that is crucial for many high-demand lucrative career fields such as:

Computer Science
Data Science
Actuarial Science
Financial Mathematics
Cryptography
Engineering
Computer Graphics
Economics

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:

Inner Product Spaces
Linear Transformations
Eigenvalues and Eigenvectors
Symmetric Matrices and Orthogonal Diagonalization
Quadratic Forms
Singular Value Decomposition

After taking this course, you will feel CARE-FREE AND CONFIDENT. I will break it all down into bite-sized no-brainer 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!

Who this course is for:

Working Professionals
Anyone interested in gaining mastery of the core concepts in Linear Algebra.
Adult Learners
College Students

Linear Algebra for Beginners: Open Doors to Great Careers 2

What you'll learn

Explore related topics

Course content

Introduction1 lecture • 4min

Inner Product Spaces23 lectures • 3hr 34min

Linear Transformations24 lectures • 2hr 56min

Eigenvalues and Eigenvectors16 lectures • 2hr 8min

Symmetric Matrices and Orthogonal Diagonalization18 lectures • 2hr 23min

Application of SVD to Statistics: Principal Component Analysis3 lectures • 29min

Conclusion2 lectures • 2min

Requirements

Description

Who this course is for: