Linear algebra #2: spaces, systems of equations, determinant, inverse
Mike X Cohen, Neuroscientist, teacher, writer


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/leftnull 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 
Pseudoinverse, part 1
7:58

About This Class
This class follows from Linear algebra #1.
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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...