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2020-11-23 16:30:15
30-Day Money-Back Guarantee

This course includes:

  • 33 hours on-demand video
  • 14 articles
  • 14 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
Teaching & Academics Math Linear Algebra

Complete linear algebra: theory and implementation in code

Learn concepts in linear algebra and matrix analysis, and implement them in MATLAB and Python.
Rating: 4.7 out of 54.7 (2,836 ratings)
18,280 students
Created by Mike X Cohen
Last updated 1/2021
English
English [Auto], Italian [Auto], 
30-Day Money-Back Guarantee

What you'll learn

  • Understand theoretical concepts in linear algebra, including proofs
  • Implement linear algebra concepts in scientific programming languages (MATLAB, Python)
  • Apply linear algebra concepts to real datasets
  • Ace your linear algebra exam!
  • Apply linear algebra on computers with confidence
  • Gain additional insights into solving problems in linear algebra, including homeworks and applications
  • Be confident in learning advanced linear algebra topics
  • Understand some of the important maths underlying machine learning
  • The math underlying most of AI (artificial intelligence)
Curated for the Udemy for Business collection

Requirements

  • Basic understanding of high-school algebra (e.g., solve for x in 2x=5)
  • Interest in learning about matrices and vectors!
  • (optional) Computer with MATLAB, Octave, or Python (or Jupyter)

Description

You need to learn linear algebra!

Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on.

You need to know applied linear algebra, not just abstract linear algebra!

The way linear algebra is presented in 30-year-old textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the "determinant" of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you, and it's in this course!

If you are interested in learning the mathematical concepts linear algebra and matrix analysis, but also want to apply those concepts to data analyses on computers (e.g., statistics or signal processing), then this course is for you! You'll see all the maths concepts implemented in MATLAB and in Python.

Unique aspects of this course

  • Clear and comprehensible explanations of concepts and theories in linear algebra.

  • Several distinct explanations of the same ideas, which is a proven technique for learning.

  • Visualization using graphs, numbers, and spaces that strengthens the geometric intuition of linear algebra.

  • Implementations in MATLAB and Python. Com'on, in the real world, you never solve math problems by hand! You need to know how to implement math in software!

  • Beginning to intermediate topics, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.

  • Strong focus on modern applications-oriented aspects of linear algebra and matrix analysis.

  • Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.

  • Improve your coding skills! You do need to have a little bit of coding experience for this course (I do not teach elementary Python or MATLAB), but you will definitely improve your scientific and data analysis programming skills in this course. Everything is explained in MATLAB and in Python (mostly using numpy and matplotlib; also sympy and scipy and some other relevant toolboxes).

Benefits of learning linear algebra

  • Understand statistics including least-squares, regression, and multivariate analyses.

  • Improve mathematical simulations in engineering, computational biology, finance, and physics.

  • Understand data compression and dimension-reduction (PCA, SVD, eigendecomposition).

  • Understand the math underlying machine learning and linear classification algorithms.

  • Deeper knowledge of signal processing methods, particularly filtering and multivariate subspace methods.

  • Explore the link between linear algebra, matrices, and geometry.

  • Gain more experience implementing math and understanding machine-learning concepts in Python and MATLAB.

  • Linear algebra is a prerequisite of machine learning and artificial intelligence (A.I.).

Why I am qualified to teach this course:

I have been using linear algebra extensively in my research and teaching (in MATLAB and Python) for many years. I have written several textbooks about data analysis, programming, and statistics, that rely extensively on concepts in linear algebra. 

So what are you waiting for??

Watch the course introductory video and free sample videos to learn more about the contents of this course and about my teaching style. If you are unsure if this course is right for you and want to learn more, feel free to contact with me questions before you sign up.

I hope to see you soon in the course!

Mike


Who this course is for:

  • Anyone interested in learning about matrices and vectors
  • Students who want supplemental instruction/practice for a linear algebra course
  • Engineers who want to refresh their knowledge of matrices and decompositions
  • Biologists who want to learn more about the math behind computational biology
  • Data scientists (linear algebra is everywhere in data science!)
  • Statisticians
  • Someone who wants to know the important math underlying machine learning
  • Someone who studied theoretical linear algebra and who wants to implement concepts in computers
  • Computational scientists (statistics, biological, engineering, neuroscience, psychology, physics, etc.)
  • Someone who wants to learn about eigendecomposition, diagonalization, and singular value decomposition!
  • Artificial intelligence students

Featured review

Denys Zaiats
Denys Zaiats
19 courses
9 reviews
Rating: 5.0 out of 5a year ago
At this age of machine learning and artificial intelligence it is really difficult to imagine the developing of the new smart applications without a knowledge of mathematics. So I decided to refresh my knowledge of linear algebra and improve my skills in machine learning. This course has plenty of useful information and approaches that are required in artificial intelligence and data science. Thank you for preparing such a great materials!

Course content

15 sections • 180 lectures • 32h 51m total length

  • What is linear algebra?
    Preview08:03
  • Linear algebra applications
    05:57
  • An enticing start to a linear algebra course!
    12:01
  • Preview03:59
  • Maximizing your Udemy experience
    07:57
  • Using MATLAB, Octave, or Python in this course
    07:54

  • Exercises + code
    00:02
  • Algebraic and geometric interpretations of vectors
    12:45
  • Vector addition and subtraction
    08:26
  • Vector-scalar multiplication
    09:07
  • Vector-vector multiplication: the dot product
    10:11
  • Dot product properties: associative, distributive, commutative
    18:55
  • Code challenge: dot products with matrix columns
    08:45
  • Code challenge: is the dot product commutative?
    09:32
  • Vector length
    06:42
  • Vector length in MATLAB
    1 question
  • Vector length in Python
    1 question
  • Preview23:38
  • Vector orthogonality
    1 question
  • Relative vector angles
    1 question
  • Code challenge: dot product sign and scalar multiplication
    12:05
  • Vector Hadamard multiplication
    03:43
  • Outer product
    10:17
  • Vector cross product
    09:05
  • Vectors with complex numbers
    08:17
  • Hermitian transpose (a.k.a. conjugate transpose)
    16:21
  • Interpreting and creating unit vectors
    07:58
  • Preview13:33
  • Dimensions and fields in linear algebra
    07:54
  • Subspaces
    15:50
  • Subspaces vs. subsets
    05:47
  • Span
    13:29
  • In the span?
    1 question
  • Linear independence
    15:34
  • Basis
    11:51

  • Exercises + code
    00:02
  • Matrix terminology and dimensionality
    08:14
  • Matrix sizes and dimensionality
    1 question
  • A zoo of matrices
    17:19
  • Can the matrices be concatenated?
    1 question
  • Matrix addition and subtraction
    08:28
  • Matrix-scalar multiplication
    02:33
  • Code challenge: is matrix-scalar multiplication a linear operation?
    07:28
  • Transpose
    10:24
  • Complex matrices
    01:51
  • Addition, equality, and transpose
    1 question
  • Diagonal and trace
    09:07
  • Code challenge: linearity of trace
    09:37
  • Broadcasting matrix arithmetic
    14:13

  • Exercises + code
    00:03
  • Introduction to standard matrix multiplication
    10:27
  • Four ways to think about matrix multiplication
    11:55
  • Code challenge: matrix multiplication by layering
    09:45
  • Matrix multiplication with a diagonal matrix
    03:42
  • Order-of-operations on matrices
    08:15
  • Matrix-vector multiplication
    16:43
  • Find the missing value!
    1 question
  • 2D transformation matrices
    15:32
  • Code challenge: Pure and impure rotation matrices
    12:38
  • Code challenge: Geometric transformations via matrix multiplications
    15:58
  • Additive and multiplicative matrix identities
    06:19
  • Additive and multiplicative symmetric matrices
    15:16
  • Hadamard (element-wise) multiplication
    05:00
  • Matrix operation equality
    1 question
  • Code challenge: symmetry of combined symmetric matrices
    12:03
  • Multiplication of two symmetric matrices
    13:21
  • Code challenge: standard and Hadamard multiplication for diagonal matrices
    06:27
  • Code challenge: Fourier transform via matrix multiplication!
    11:20
  • Frobenius dot product
    11:16
  • Matrix norms
    18:11
  • Code challenge: conditions for self-adjoint
    11:52
  • What about matrix division?
    04:24

  • Exercises + code
    00:02
  • Rank: concepts, terms, and applications
    10:50
  • Maximum possible rank.
    1 question
  • Computing rank: theory and practice
    23:01
  • Rank of added and multiplied matrices
    11:46
  • What's the maximum possible rank?
    1 question
  • Code challenge: reduced-rank matrix via multiplication
    10:38
  • Code challenge: scalar multiplication and rank
    12:10
  • Rank of A^TA and AA^T
    10:41
  • Code challenge: rank of multiplied and summed matrices
    07:06
  • Making a matrix full-rank by "shifting"
    14:12
  • Code challenge: is this vector in the span of this set?
    11:46
  • Course tangent: self-accountability in online learning
    03:03

  • Exercises + code
    00:00
  • Column space of a matrix
    13:29
  • Column space, visualized in code
    06:35
  • Row space of a matrix
    04:25
  • Null space and left null space of a matrix
    14:39
  • Column/left-null and row/null spaces are orthogonal
    10:47
  • Dimensions of column/row/null spaces
    08:10
  • Example of the four subspaces
    11:09
  • More on Ax=b and Ax=0
    07:52

  • Exercises + code
    00:01
  • Preview19:39
  • Converting systems of equations to matrix equations
    04:23
  • Gaussian elimination
    14:42
  • Echelon form and pivots
    07:21
  • Reduced row echelon form
    18:29
  • Code challenge: RREF of matrices with different sizes and ranks
    12:16
  • Matrix spaces after row reduction
    09:23

  • Exercises
    00:01
  • Determinant: concept and applications
    05:59
  • Determinant of a 2x2 matrix
    07:03
  • Code challenge: determinant of small and large singular matrices
    11:07
  • Determinant of a 3x3 matrix
    13:13
  • Code challenge: large matrices with row exchanges
    06:32
  • Find matrix values for a given determinant
    04:51
  • Code challenge: determinant of shifted matrices
    18:27
  • Code challenge: determinant of matrix product
    10:37

  • Exercises + code
    00:02
  • Matrix inverse: Concept and applications
    12:40
  • Computing the inverse in code
    06:31
  • Inverse of a 2x2 matrix
    07:55
  • The MCA algorithm to compute the inverse
    13:58
  • Code challenge: Implement the MCA algorithm!!
    18:39
  • Computing the inverse via row reduction
    16:40
  • Code challenge: inverse of a diagonal matrix
    10:50
  • Preview10:14
  • One-sided inverses in code
    12:40
  • Proof: the inverse is unique
    03:16
  • Pseudo-inverse, part 1
    11:34
  • Code challenge: pseudoinverse of invertible matrices
    06:02

  • Exercises + code
    00:02
  • Projections in R^2
    09:59
  • Projections in R^N
    15:24
  • Orthogonal and parallel vector components
    12:38
  • Code challenge: decompose vector to orthogonal components
    16:40
  • Orthogonal matrices
    12:02
  • Gram-Schmidt procedure
    12:43
  • QR decomposition
    20:59
  • Code challenge: Gram-Schmidt algorithm
    20:35
  • Preview01:45
  • Code challenge: Inverse via QR
    14:19
  • Code challenge: Prove and demonstrate the Sherman-Morrison inverse
    17:26
  • Code challenge: A^TA = R^TR
    06:00

Instructor

Mike X Cohen
Neuroscientist, writer, professor
Mike X Cohen
  • 4.5 Instructor Rating
  • 20,437 Reviews
  • 103,150 Students
  • 20 Courses

I am a neuroscientist (brain scientist) and associate professor at the Radboud University in the Netherlands. I have an active research lab that has been funded by the US, German, and Dutch governments, European Union, hospitals, and private organizations.

But you're here because of my teaching, so let me tell you about that: 

I have 20 years of experience teaching programming, data analysis, signal processing, statistics, linear algebra, and experiment design. I've taught undergraduate students, PhD candidates, postdoctoral researchers, and full professors. I teach in "traditional" university courses, special week-long intensive courses, and Nobel prize-winning research labs. I have >80 hours of online lectures on neuroscience data analysis that you can find on my website and youtube channel. And I've written several technical books about these topics with a few more on the way.

I'm not trying to show off -- I'm trying to convince you that you've come to the right place to maximize your learning from an instructor who has spent two decades refining and perfecting his teaching style.

Over 94,000 students have watched over 6,500,000 minutes of my courses (that's over 12 years of continuous learning). Come find out why!

I have several free courses that you can enroll in. Try them out! You got nothing to lose ;)

                                                  -------------------------

By popular request, here are suggested course progressions for various educational goals:

MATLAB programming: MATLAB onramp; Master MATLAB; Image Processing

Python programming: Master Python programming by solving scientific projects; Master Math by Coding in Python

Applied linear algebra: Complete Linear Algebra; Dimension Reduction

Signal processing: Understand the Fourier Transform; Generate and visualize data; Signal Processing; Neural signal processing

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