Linear algebra #1: Vectors and matrices
Mike X Cohen, Neuroscientist, teacher, writer


Target audience for this course
4:07 
What is linear algebra
6:54 
Linear algebra applications
5:37 
How best to learn from this course
3:49 
Using Jupyter online for Python code (no installation necessary!)
3:53 
Algebraic and geometric interpretations
10:52 
Vector addition and subtraction
6:32 
Vectorscalar multiplication
7:15 
Vectorvector multiplication: the dot product
8:35 
Vector length
5:18 
Dot product geometry: sign and orthogonality
12:55 
Code challenge: dot product sign and scalar multiplication
9:21 
Outer product
6:07 
Interpreting and creating unit vectors
5:04 
Code challenge: dot products with unit vectors
8:48 
Dimensions and fields in linear algebra
7:11 
Subspaces
14:35 
Subspaces vs. subsets
5:25 
Span
11:19 
Linear independence
15:25 
Basis
10:22 
Matrix terminology and dimensionality
7:33 
A zoo of matrices
9:34 
Matrix addition and subtraction
4:27 
Matrixscalar multiplication
1:48 
Transpose
6:00 
Diagonal and trace
4:59 
Code challenge: linearity of trace
6:48 
Intro to standard matrix multiplication
6:56 
4 ways to think about matrix multiplication
9:37 
Code challenge: matrix multiplication by layering
6:10 
Matrix multiplication with a diagonal matrix
2:51 
Orderofoperations on matrices
6:51 
Matrixvector multiplication
8:33 
2D transformation matrices
12:35 
Additive and multiplicative matrix identities
3:49 
Additive and multiplicative symmetric matrices
10:50 
Hadamard (elementwise) multiplication
2:01 
Code challenge: symmetry of combined symmetric matrices
9:08 
Code challenge: standard and Hadamard multiplication for diagonal matrices
3:48 
Frobenius dot product
7:35 
What about matrix division?
4:08 
Rank: concepts, terms, and applications
9:58 
Computing rank: theory and practice
11:59 
Rank of added and multiplied matrices
11:01 
Rank of A^TA and AA^T
9:13 
Code challenge: rank of multiplied and summed matrices
7:10 
Code challenge: scalar multiplication does not change rank
7:08 
Making a matrix fullrank by “shifting”
6:56

About This Class
Linear algebra is one of the most important topics in mathematics for modern computational sciences. Linear algebra is the basis for machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, and so on.
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, then this course is for you! 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!
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Officially I'm Dr. Michael X Cohen, but I prefer just "Mike" or "Mike X" or "the mysterious X." I'm a scientist because I believe that discovery and the drive to understand mysteries are among the most important drivers of progress in human civilization. And I believe in teaching because, well, because I really like teaching. I've been doing it my whole life. I teach "reallife" courses, online courses, university courses. I've written several books about neuroscience and data analysis, which...