Determinant, Trace and Eigenvalues of a Matrix @thrustofcuriosity5407

Thrust of curiosity
Determinant, Trace, and eigenvalues of a Matrix

Videos for your reference
Operations on matrix -

What did we discuss in this video? (with timecodes)

0:00 - Intro
0:35 - determinant of 2x2 matrix
1:25 - finding a trace of a matrix
2:02 - finding the eigenvalue of a matrix
4:04 - finding roots of quadratic equations
6:10 - relation between determinant, trace, and eigenvalues
8:20 - determinant, trace, and eigenvalues of the triangular (or diagonal) matrix
9:00 - trick to find eigenvalues
11:25 - eigenvalues of 3x3 matrix
11:56 - determinant of 3x3 triangular matrix
12:30 - conventional method (expansion through the first row)
13:40 - expansion through any other row or column
18:55 - synthetic division method

Tricks learned in the video
1) Expansion of a determinant through any row or any column
2) Eigenvalues of a triangular or diagonal matrix
3) Relation between determinant, trace, and eigenvalues
trace = sum of all diagonal elements = sum of all eigenvalues
determinant = product of all eigenvalues


#tricks
#trending
#mathematics
#mathematicalphysics
#thrustofcuriosity