Linear algebra #2: spaces, systems of equations, determinant, inverse | Mike X Cohen | Skillshare

# Linear algebra #2: spaces, systems of equations, determinant, inverse

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

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28 Videos (4h 19m)
• Column space of a matrix

15:21
• Row space of a matrix

4:31
• Null space and left null space of a matrix

13:20
• Column/left-null and row/null spaces are orthogonal

6:59
• Dimensions of column/row/null spaces

5:57
• Example of the four subspaces

10:00
• More on Ax=b and Ax=0

7:08
• Systems of equations: algebra and geometry

14:32
• Converting systems of equations to matrix equations

5:37
• Gaussian elimination

12:06
• Echelon form and pivots

7:14
• Reduced row echelon form

12:57
• Code challenge: RREF of matrices with different sizes and ranks

8:40
• Matrix spaces after row reduction

7:44
• Determinant: concept and applications

6:30
• Code challenge: determinant of small and large singular matrices

6:31
• Determinant of a 2x2 matrix

7:03
• Determinant of a 3x3 matrix

10:52
• Code challenge: determinant of shifted matrices

12:15
• Find matrix values for a given determinant

4:57
• Matrix inverse: Concept and applications

11:31
• Inverse of a 2x2 matrix

5:36
• The MCA algorithm to compute the inverse

11:04
• Computing the inverse via row reduction

16:52
• Code challenge: inverse of a diagonal matrix

9:09
• Left inverse and right inverse

13:50
• Proof: the inverse is unique

3:00
• Pseudo-inverse, part 1

7:58

This class follows from Linear algebra #1.

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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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