Questions tagged [linear-algebra]
For questions on linear algebra, including vector spaces, linear transformations, systems of linear equations, spanning sets, bases, dimensions and vector subspaces.
130,752 questions
1 vote
1 answer
33 views
Does the tensor $\Phi$ take this form?
We will use Einstein summation convention. I apologize if this question is too easy—it has been years since I've had to to work with some of the mentioned material. Have the the set of all linear ...
- 1,881
1 vote
1 answer
76 views
Why is fact that the determinant of this matrix is 0 equivalent to $x'^T Fx=0$
I am reading Multiple View Geometry in Computer Vision and in the chapter 17.1, it talks about the following matrix which needs to have $0$ determinant. $$ \begin{bmatrix} A & x & \textbf{0} \\...
- 11
0 votes
0 answers
16 views
Levinson Recursion With Sub-Singular Hermitian Toeplitz Matrices Fails for Complex Inputs [closed]
I’m trying to implement the Levinson recursion for Hermitian Toeplitz systems, including cases where some leading principal minors are (nearly) singular. The implementation works for real-valued ...
-5 votes
0 answers
38 views
Looking for Math Major Scholarships in the US or Europe [closed]
I’m planning to apply for a bachelor’s degree in Mathematics and I’m trying to find good scholarship options in either the United States or Europe. I’ve been checking individual university websites, ...
0 votes
0 answers
43 views
Unit Vectors in Polar Coordinate System [closed]
What is the need for different sets of unit vector for different locations (positions) in Polar Coordinate System ? Just as the two fixed unit vectors in Cartesian Coordinate System, why cannot we ...
- 1
0 votes
1 answer
68 views
Is there an intuitive way to understand this formula for the magnitude of the projection of one vector onto another? [duplicate]
Let's say it's 200 B.C. and you're tasked with building all of modern math from the ground up. Let's say also that we already intuitively understand the concepts of a "vector", the "...
2 votes
0 answers
60 views
Can one prove that two 2-forms with the same kernel are proportional to one another in this specific setting?
My name is Sarah and I am currently writing my Bachelorthesis about the paper A property of conformally Hamiltonian vector fields; application to the Kepler problem by Charles-Michel Marle (2012). You ...
- 21
1 vote
1 answer
62 views
Is $||B(A + B + C)^{-1}|| \le ||B(A+B)^{-1}||$ for positive semi-definite matrices?
Let $A,B,C \in \mathbb{R}^{d \times d}$ be symmetric positive semi-definite with $A$ strictly positive definite. Is it true that $$||BM^{-1}||_2 \le ||BN^{-1}||_2, \quad M := A + B + C, \quad N := A + ...
- 1,216