Mô tả

HOW BECOME A LINEAR ALGEBRA MASTER IS SET UP TO MAKE COMPLICATED MATH EASY:

This 247-lesson course includes video and text explanations of everything from Linear Algebra, and it includes 69 quizzes (with solutions!) and an additional 12 workbooks with extra practice problems, to help you test your understanding along the way. Become a Linear Algebra Master is organized into the following sections:

  • Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination

  • Operations on two matrices, including matrix multiplication and elimination matrices

  • Matrices as vectors, including linear combinations and span, linear independence, and subspaces

  • Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities

  • Matrix-vector products, including the null and column spaces, and solving Ax=b

  • Transformations, including linear transformations, projections, and composition of transformations

  • Inverses, including invertible and singular matrices, and solving systems with inverse matrices

  • Determinants, including upper and lower triangular matrices, and Cramer's rule

  • Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose

  • Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis

  • Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process

  • Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions



AND HERE'S WHAT YOU GET INSIDE OF EVERY SECTION:

Videos: Watch over my shoulder as I solve problems for every single math issue you’ll encounter in class. We start from the beginning... I explain the problem setup and why I set it up that way, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.

Notes: The notes section of each lesson is where you find the most important things to remember. It’s like Cliff Notes for books, but for math. Everything you need to know to pass your class and nothing you don’t.

Quizzes: When you think you’ve got a good grasp on a topic within a course, you can test your knowledge by taking one of the quizzes. If you pass, great! If not, you can review the videos and notes again or ask for help in the Q&A section.

Workbooks: Want even more practice? When you've finished the section, you can review everything you've learned by working through the bonus workbook. The workbooks include tons of extra practice problems, so they're a great way to solidify what you just learned in that section.



HERE'S WHAT SOME STUDENTS OF BECOME A LINEAR ALGEBRA MASTER HAVE TOLD ME:

  • “Another fantastic course. Provides an academic foundation of linear algebra to prepare for applied or programming-based courses.” - Christopher C.

  • “I have no words to thank Krista for this amazing course, I was really overwhelmed because I had to take a test for a class I couldn't attend and I didn't know anything about linear algebra and surprisingly this course was what I needed, reading the notes before watching the video helped to understand by myself and when I was lost the video content was a great resource, I got a 9 out of 10 in the test, so I highly recommend to take this course, Krista is such a good teacher.” - Alan M.

  • “I started out as a math major in college, and dropped my major during linear algebra. I wish I had this class and this instructor in college. I might have stuck with my major.” - Eric L.

  • “Notes are great, explanations are clear and starting from the beginning. Terrific so far.” - Phil T.

  • “Very clear and has not skipped any steps. If the rest of the course is like this, I will pass my class with no problem.” - Brandon P.

  • “Really well structured and well explained, and there are plenty of exercises to reinforce the knowledge.” - Ashfaque C.



YOU'LL ALSO GET:

  • Lifetime access to Become a Linear Algebra Master

  • Friendly support in the Q&A section

  • Udemy Certificate of Completion available for download

  • 30-day money back guarantee


Enroll today!

I can't wait for you to get started on mastering Linear Algebra.

- Krista :)

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14 sections

Getting started

4 lectures
What we'll learn in this course
04:40
How to get the most out of this course
01:26
Download the formula sheet
00:19
The EVERYTHING download
00:24

Operations on one matrix

27 lectures
Introduction to operations on one matrix
01:24
RESOURCE: Quiz solutions for this section
00:17
Linear systems in two unknowns
00:00
Linear systems in two unknowns
12:15
Linear systems in two unknowns
3 questions
Linear systems in three unknowns
00:00
Linear systems in three unknowns
10:20
Linear systems in three unknowns
3 questions
Matrix dimensions and entries
00:00
Matrix dimensions and entries
06:07
Matrix dimensions and entries
3 questions
Representing systems with matrices
00:00
Representing systems with matrices
09:58
Representing systems with matrices
3 questions
Simple row operations
00:00
Simple row operations
10:14
Simple row operations
3 questions
Pivot entries and row-echelon forms
00:00
Pivot entries and row-echelon forms
16:17
Pivot entries and row-echelon forms
3 questions
Gauss-Jordan elimination
00:00
Gauss-Jordan elimination
13:56
Gauss-Jordan elimination
3 questions
Number of solutions to the linear system
00:00
Number of solutions to the linear system
13:19
Number of solutions to the linear system
3 questions
BONUS! Extra practice problems. :)
00:26

Operations on two matrices

21 lectures
Introduction to operations on two matrices
01:17
RESOURCE: Quiz solutions for this section
00:17
Matrix addition and subtraction
00:00
Matrix addition and subtraction
09:48
Matrix addition and subtraction
3 questions
Scalar multiplication
00:00
Scalar multiplication
06:04
Scalar multiplication
3 questions
Zero matrices
00:00
Zero matrices
04:06
Zero matrices
3 questions
Matrix multiplication
00:00
Matrix multiplication
11:51
Matrix multiplication
3 questions
Identity matrices
00:00
Identity matrices
09:23
Identity matrices
3 questions
The elimination matrix
00:00
The elimination matrix
13:19
The elimination matrix
3 questions
BONUS! Extra practice problems. :)
00:26

Matrices as vectors

30 lectures
Introduction to matrices as vectors
01:17
RESOURCE: Quiz solutions for this section
00:17
Vectors
Processing..
Vectors
08:54
Vectors
3 questions
Vector operations
00:00
Vector operations
10:49
Vector operations
3 questions
Unit vectors and basis vectors
Processing..
Unit vectors and basis vectors
16:10
Unit vectors and basis vectors
3 questions
Linear combinations and span
00:00
Linear combinations and span
13:28
Linear combinations and span
3 questions
Linear independence in two dimensions
Processing..
Linear independence in two dimensions
13:55
Linear independence in two dimensions
3 questions
Linear independence in three dimensions
00:00
Linear independence in three dimensions
09:38
Linear independence in three dimensions
3 questions
Linear subspaces
00:00
Linear subspaces
13:38
Linear subspaces
3 questions
Spans as subspaces
00:00
Spans as subspaces
09:22
Spans as subspaces
3 questions
Basis
00:00
Basis
17:15
Basis
3 questions
BONUS! Extra practice problems. :)
00:26

Dot products and cross products

24 lectures
Introduction to dot products and cross products
01:11
RESOURCE: Quiz solutions for this section
00:17
Dot products
00:00
Dot products
10:35
Dot products
3 questions
Cauchy-Schwarz inequality
Processing..
Cauchy-Schwarz inequality
08:05
Cauchy-Schwarz inequality
3 questions
Vector triangle inequality
00:00
Vector triangle inequality
10:27
Vector triangle inequality
3 questions
Angle between vectors
00:00
Angle between vectors
09:04
Angle between vectors
3 questions
Equation of a plane, and normal vectors
00:00
Equation of a plane, and normal vectors
09:09
Equation of a plane, and normal vectors
3 questions
Cross products
00:00
Cross products
14:23
Cross products
3 questions
Dot and cross products as opposite ideas
00:00
Dot and cross products as opposite ideas
13:38
Dot and cross products as opposite ideas
3 questions
BONUS! Extra practice problems. :)
00:26

Matrix-vector products

21 lectures
Introduction to matrix-vector products
01:09
RESOURCE: Quiz solutions for this section
00:17
Multiplying matrices by vectors
00:00
Multiplying matrices by vectors
08:32
Multiplying matrices by vectors
3 questions
The null space and Ax=O
00:00
The null space and Ax=O
20:24
The null space and Ax=O
3 questions
Null space of a matrix
00:00
Null space of a matrix
16:20
Null space of a matrix
3 questions
The column space and Ax=b
Processing..
The column space and Ax=b
17:17
The column space and Ax=b
3 questions
Solving Ax=b
Processing..
Solving Ax=b
23:52
Solving Ax=b
3 questions
Dimensionality, nullity, and rank
Processing..
Dimensionality, nullity, and rank
09:40
Dimensionality, nullity, and rank
3 questions
BONUS! Extra practice problems. :)
00:26

Transformations

27 lectures
Introduction to transformations
01:22
RESOURCE: Quiz solutions for this section
00:16
Functions and transformations
00:00
Functions and transformations
12:42
Functions and transformations
3 questions
Transformation matrices and the image of the subset
00:00
Transformation matrices and the image of the subset
19:28
Transformation matrices and the image of the subset
3 questions
Preimage, image, and the kernel
00:00
Preimage, image, and the kernel
10:15
Preimage, image, and the kernel
3 questions
Linear transformations as matrix-vector products
00:00
Linear transformations as matrix-vector products
14:49
Linear transformations as matrix-vector products
3 questions
Linear transformations as rotations
00:00
Linear transformations as rotations
05:48
Linear transformations as rotations
3 questions
Adding and scaling linear transformations
00:00
Adding and scaling linear transformations
09:29
Adding and scaling linear transformations
3 questions
Projections as linear transformations
00:00
Projections as linear transformations
15:52
Projections as linear transformations
3 questions
Compositions of linear transformations
00:00
Compositions of linear transformations
10:00
Compositions of linear transformations
3 questions
BONUS! Extra practice problems. :)
00:26

Inverses

18 lectures
Introduction to inverses
01:27
RESOURCE: Quiz solutions for this section
00:16
Inverse of a transformation
00:00
Inverse of a transformation
14:39
Inverse of a transformation
3 questions
Invertibility from the matrix-vector product
00:00
Invertibility from the matrix-vector product
18:18
Invertibility from the matrix-vector product
3 questions
Inverse transformations are linear
00:00
Inverse transformations are linear
09:54
Inverse transformations are linear
3 questions
Matrix inverses, and invertible and singular matrices
Processing..
Matrix inverses, and invertible and singular matrices
11:36
Matrix inverses, and invertible and singular matrices
3 questions
Solving systems with inverse matrices
00:00
Solving systems with inverse matrices
08:39
Solving systems with inverse matrices
3 questions
BONUS! Extra practice problems. :)
00:26

Determinants

18 lectures
Introduction to determinants
00:55
RESOURCE: Quiz solutions for this section
00:16
Determinants
00:00
Determinants
20:21
Determinants
3 questions
Cramer's rule for solving systems
00:00
Cramer's rule for solving systems
15:47
Cramer's rule for solving systems
3 questions
Modifying determinants
00:00
Modifying determinants
09:52
Modifying determinants
3 questions
Upper and lower triangular matrices
00:00
Upper and lower triangular matrices
16:59
Upper and lower triangular matrices
3 questions
Using determinants to find area
00:00
Using determinants to find area
08:27
Using determinants to find area
3 questions
BONUS! Extra practice problems. :)
00:26

Transposes

18 lectures
Introduction to transposes
00:58
RESOURCE: Quiz solutions for this section
00:16
Transposes and their determinants
00:00
Transposes and their determinants
09:14
Transposes and their determinants
3 questions
Transposes of products, sums, and inverses
00:00
Transposes of products, sums, and inverses
12:39
Transposes of products, sums, and inverses
3 questions
Null and column spaces of the transpose
00:00
Null and column spaces of the transpose
21:21
Null and column spaces of the transpose
3 questions
The product of a matrix and its transpose
00:00
The product of a matrix and its transpose
07:04
The product of a matrix and its transpose
3 questions
A=LU factorization
Processing..
A=LU factorization
33:24
A=LU factorization
3 questions
BONUS! Extra practice problems. :)
00:26

Orthogonality and change of basis

21 lectures
Introduction to orthogonality and change of basis
01:29
RESOURCE: Quiz solutions for this section
00:17
Orthogonal complements
00:00
Orthogonal complements
15:35
Orthogonal complements
3 questions
Orthogonal complements of the fundamental subspaces
00:00
Orthogonal complements of the fundamental subspaces
15:49
Orthogonal complements of the fundamental subspaces
3 questions
Projection onto the subspace
00:00
Projection onto the subspace
18:35
Projection onto the subspace
3 questions
Least squares solution
00:00
Least squares solution
18:52
Least squares solution
3 questions
Coordinates in a new basis
00:00
Coordinates in a new basis
15:32
Coordinates in a new basis
3 questions
Transformation matrix for a basis
00:00
Transformation matrix for a basis
14:32
Transformation matrix for a basis
3 questions
BONUS! Extra practice problems. :)
00:26

Orthonormal bases and Gram-Schmidt

12 lectures
Introduction to orthonormal bases and Gram-Schmidt
01:09
RESOURCE: Quiz solutions for this section
00:17
Orthonormal bases
00:00
Orthonormal bases
09:49
Orthonormal bases
3 questions
Projection onto an orthonormal basis
00:00
Projection onto an orthonormal basis
09:05
Projection onto an orthonormal basis
3 questions
Gram-Schmidt process for change of basis
00:00
Gram-Schmidt process for change of basis
16:56
Gram-Schmidt process for change of basis
3 questions
BONUS! Extra practice problems. :)
00:26

Eigenvalues and Eigenvectors

9 lectures
Introduction to Eigenvalues and Eigenvectors
00:56
RESOURCE: Quiz solutions for this section
00:17
Eigenvalues, eigenvectors, eigenspaces
00:00
Eigenvalues, eigenvectors, eigenspaces
21:33
Eigenvalues, eigenvectors, eigenspaces
3 questions
Eigen in three dimensions
00:00
Eigen in three dimensions
16:09
Eigen in three dimensions
3 questions
BONUS! Extra practice problems. :)
00:26

Final exam and wrap-up

4 lectures
Practice final exam #1 (optional)
00:35
Practice final exam #2 (optional)
00:35
Linear Algebra final exam
00:31
Wrap-up
00:24

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