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.
Class Projects See All
No projects have
been added yet
No projects have
been added yet
No projects have
been added yet
No projects have
been added yet
Students
Projects

 
 Beginner
 Intermediate
 Advanced
 All Levels
 Beg/Int
 Int/Adv
Level
Community Generated
The level is determined by a majority opinion of students who have reviewed this class. The teacher's recommendation is shown until at least 5 student responses are collected.
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...