Minimal polynomials and characteristic polynomials?
I am trying to understand the similarities and differences between the minimal polynomial and characteristic polynomial of Matrices. 1. When are the minimal polynomial and characteristic... more
Proof that the Trace of a Matrix is the sum of its Eigenvalues?
I have looked extensively for a proof on the internet but all of them were too obscure. I would appreciate if someone could lay out a simple proof for this important result. Thank you.
Would it be useful to have a method of solving any solvable problem?
I have a question about how to find a basis for a subspace in (Linear Algebra) ,like how to find a basis for the kernel?And how to find a basis for the range?
Or finding a basis for any subspace , like .... can I find a basis for any subspace or does it have some kinda conditions ? It's really confusing me ...
Can you explain vector projection and why projᵥu= (<u,v>/<v, v>) v? What's the connection between the algebraic formula and the geometric meaning?
Must eigenvalues be numbers?
This is more a conceptual question than any other kind. As far as I know, one can define matrices over arbitrary fields, and so do linear algebra in different settings than in the typical... more
assume y is a differentiable function of x and dy/dx - sin(ay) + cos(bx)=xy
Find the function g(x) such that f(x) is equal to (x^3-3)/g(x) given the following conditions
There is NO Vertical asymptotesThere is a slant asymptote y=x
For which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions?
Determine for which values parameter x,y system equations with two unknowns have unique solution,inconsistent or infinitely many solutions. ax+by=c^2 a+x/b=b+y/a , a≠o,b≠o and another... more