Linear Algebra for Beginners: Open Doors to Great Careers 2

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

1,244 students enrolled

What Will I 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.

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 is the target audience?

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

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Curriculum For This Course

87 Lectures

11:37:21
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Introduction
1 Lecture
04:00

Preview
04:00

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Inner Product Spaces
23 Lectures
03:15:50

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.

Preview
17:01

The notion of the distance between two vectors is introduced.

Students will learn how to find the distance between two vectors.

Distance Between Vectors in Rn

09:20

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.

Angle Between Vectors in Rn

19:57

Practice problems for norms and dot product for Rn.

Problem Set: Norms and Dot Product for Rn

1 page

Solutions to Problem Set: Norms and Dot Product for Rn

Solutions to Problem Set: Norms and Dot Product for Rn

2 pages

The definitions of inner product and of inner product spaces are provided.

Inner Product Spaces

11:08

Students will learn about some examples of inner product and of inner product spaces.

Examples of Inner Product

12:34

The definitions of norm, distance, and angle between two vectors in an inner product space are provided.

Norm, Distance, and Angle for Inner Product Spaces

18:56

An additional example of norm, distance, and angle for inner product spaces is provided.

Additional Example of Norm, Distance, and Angle for Inner Product Spaces

08:06

Students will learn how to find the orthogonal projection of one vector onto another vector.

Preview
12:51

Practice problems for inner product spaces.

Preview
2 pages

Solutions to Problem Set: Inner Product Spaces

Preview
2 pages

The definitions of orthogonal basis and of orthonormal basis are provided.

Orthonormal Bases

10:55

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

Coordinates Relative to an Orthonormal Basis

15:15

Students will learn what the Gram-Schmidt process is.

Preview
08:09

Students will learn how to apply the Gram-Schmidt process.

Example of Gram-Schmidt Process

12:45

An additional example of applying the Gram-Schmidt process is provided.

Additional Example of the Gram-Schmidt Process

15:42

Practice problems for orthonormal bases.

Problem Set: Orthonormal Bases

1 page

Solutions to Problem Set: Orthonormal Bases

Solutions to Problem Set: Orthonormal Bases

4 pages

The least-squares problem is introduced.

Preview
09:12

Students will learn how to solve least-squares problems.

Example of Least-Squares Problem

13:59

Practice problems for least squares problems.

Problem Set: Least Squares Problems

1 page

Solutions to Problem Set: Least Squares Problems

Solutions to Problem Set: Least Squares Problems

5 pages

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Linear Transformations
24 Lectures
02:35:17

The definition of linear transformation is provided.

Preview
14:09

Students will learn about linear transformations represented by matrices.

Linear Transformations Represented by Matrices

06:55

Practice problems for linear transformations.

Problem Set: Linear Transformations

1 page

Solutions to Problem Set: Linear Transformations

Solutions to Problem Set: Linear Transformations

2 pages

The definition of the kernel of a linear transformation is provided.

Students will learn how to find the kernel of a linear transformation.

Kernel of a Linear Transformation

13:05

Students will learn how to find a basis for the kernel of a linear transformation.

The Kernel of T as a Subspace of V

08:23

The definition of the range of a linear transformation is provided.

The Range of a Linear Transformation

05:41

Students will learn how to find a basis for the range of a linear transformation.

Finding a Basis for Range(T)

04:58

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.

Rank and Nullity of a Linear Transformation

09:47

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.

Preview
14:34

The definition of isomorphism is provided.

Isomorphisms

03:52

Practice problems for the kernel and range of a linear transformation.

Problem Set: The Kernel and Range of a Linear Transformation

2 pages

Solutions to Problem Set: The Kernel and Range of a Linear Transformation

Solutions to Problem Set: The Kernel and Range of a Linear Transformation

7 pages

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'.

Matrix Representation of Linear Transformations

14:52

Students will learn 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

Additional examples of finding the matrix of T relative to the bases B and B' are provided.

Additional Example of the Matrix of T Relative to the Bases B and B'

12:25

Practice problems for matrix representation of linear transformations.

Preview
1 page

Solutions to Problem Set: Matrix Representation of Linear Transformations

Preview
4 pages

Students will learn about reflections and rotations in the plane.

Applications of Linear Transformations

08:04

Students will learn how to apply compositions of linear transformations.

Composition of Linear Transformations

05:48

Students will learn how to apply rotations in 3-dimensional space.

Application to Computer Graphics

15:33

Practice problems for applications of linear transformations.

Problem Set: Applications of Linear Transformations

1 page

Solutions to Problem Set: Applications of Linear Transformations

Solutions to Problem Set: Applications of Linear Transformations

2 pages

Review Request

1 page

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Eigenvalues and Eigenvectors
16 Lectures
01:53:07

The definitions of eigenvalue, eigenvector, and eigenspace are provided.

Students will learn the geometric interpretation of eigenvalues and eigenvectors.

Preview
14:37

Students will learn how to find the eigenvalues and eigenvectors of a matrix.

Finding Eigenvalues and Eigenvectors of a Matrix

07:15

An example of finding eigenvalues and eigenvectors of a matrix is provided.

Preview
10:13

An additional example of finding eigenvalues and eigenvectors is provided. The notion of multiplicity of an eigenvalue is also introduced.

Additional Example of Finding Eigenvalues and Eigenvectors

14:36

Practice problems for eigenvalues and eigenvectors.

Problem Set: Eigenvalues and Eigenvectors

1 page

Solutions to Problem Set: Eigenvalues and Eigenvectors

Solutions to Problem Set: Eigenvalues and Eigenvectors

4 pages

The notion of diagonalizability is introduced.

Diagonalization

13:01

Students will learn about a necessary and sufficient condition for diagonalizability.

A Necessary and Sufficient Condition for Diagonalizability

15:30

Students will learn about a necessary and sufficient condition for diagonalizability.

A Necessary and Sufficient Condition for Diagonalizability (Continued)

05:15

Students will learn how to diagonalize a matrix.

Diagonalizing a Matrix

04:43

Practice problems for diagonalization.

Preview
1 page

Solutions to Problem Set: Diagonalization

Preview
5 pages

Students will learn how to apply diagonalization to solving a system of linear differential equations.

Applications to Differential Equations

14:19

An example of solving a system of linear differential equations is provided.

Example of Solving a System of Linear Differential Equations

13:38

Practice problems for applications to differential equations.

Problem Set: Applications to Differential Equations

1 page

Solutions to Problem Set: Applications to Differential Equations

Solutions to Problem Set: Applications to Differential Equations

3 pages

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Symmetric Matrices and Orthogonal Diagonalization
18 Lectures
02:06:55

Students will learn about the properties of symmetric matrices.

Preview
03:17

An example of verifying the properties of symmetric matrices is provided.

Example of Verifying Properties of Symmetric Matrices

17:52

The definition of orthogonal diagonalization is provided.

Students will learn how to orthogonally diagonalize a matrix.

Preview
19:54

The steps of orthogonal diagonalization are summarized.

Summary of Orthogonal Diagonalization

06:45

The properties of symmetric matrices are summarized in the Spectral Theorem for Symmetric Matrices.

The Spectral Theorem for Symmetric Matrices

03:31

Practice problems for symmetric matrices and orthogonal diagonalization.

Preview
1 page

Solutions to Problem Set: Symmetric Matrices and Orthogonal Diagonalization

Preview
5 pages

Quadratic forms are introduced, and several examples are provided.

Preview
13:07

Students will learn how to apply orthogonal diagonalization to eliminating cross-product terms in quadratic forms.

Eliminating Cross-product Terms

06:30

An example of eliminating cross-product terms in a quadratic form is provided.

Example of Eliminating Cross-product Terms

13:42

Students will learn about the Principal Axes Theorem.

The Principal Axes Theorem

05:38

Practice problems for quadratic forms.

Problem Set: Quadratic Forms

1 page

Solutions to Problem Set: Quadratic Forms

Solutions to Problem Set: Quadratic Forms

2 pages

Students will learn what a singular value decomposition of a matrix is.

Preview
08:44

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

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.

Example of Finding a Singular Value Decomposition of a Matrix (Continued)

13:50

Practice problems for singular value decomposition.

Problem Set: Singular Value Decomposition

1 page

Solutions to Problem Set: Singular Value Decomposition

Solutions to Problem Set: Singular Value Decomposition

6 pages

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Application of SVD to Statistics: Principal Component Analysis
3 Lectures
29:12

Students will learn what mean-deviation form is and what a covariance matrix is.

Mean-Deviation Form and Covariance Matrix

09:35

Students will see an illustration of mean-deviation form and covariance matrix. Students will also learn what variance is.

Illustration of Mean-Deviation Form and Covariance Matrix

09:21

The notion of principal component is introduced.

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

Principal Component Analysis

10:16

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Conclusion
2 Lectures
00:00

Concluding Letter

1 page

Bonus Lecture

2 pages

About the Instructor