Linear algebra #1: Vectors and matrices | Mike X Cohen | Skillshare

# Linear algebra #1: Vectors and matrices

#### Mike X Cohen, Neuroscientist, teacher, writer

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49 Videos (6h 9m)
• 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

6:32
• Vector-scalar multiplication

7:15
• Vector-vector 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

4:27
• Matrix-scalar 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
• Order-of-operations on matrices

6:51
• Matrix-vector multiplication

8:33
• 2D transformation matrices

12:35
• Additive and multiplicative matrix identities

3:49
• Additive and multiplicative symmetric matrices

10:50

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

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 full-rank by “shifting”

6:56

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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#### Mike X Cohen

Neuroscientist, teacher, writer

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 "real-life" courses, online courses, university courses. I've written several books about neuroscience and data analysis, which...

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