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location Waterloo, Canada
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Mathematical Physics Major at the University of Waterloo.


1d
awarded  Constituent
Dec
8
awarded  Caucus
Dec
5
comment Is there a complete list of forbidden minors of graph of genus 1?
See this Math Overflow answer. This is known for the projective plane (i.e. non-orientable genus 1 surface), and there are a total of $35$ forbidden minors. It appears that there are over $16,000$ forbidden minors for the torus, so I doubt the complete list is known for all genus.
Dec
5
comment How many decimal strings of length 55 contain exactly ten 7s?
You are close for the first part, but you need to include the positions of the 7s. Where are they in the string? Also, excluding 7 should give you 9 remaining choices, not 8 (did you include 0?). For the second part, presumably you don't care what the order the donuts are chosen in, so you need a different answer.
Dec
4
awarded  Popular Question
Dec
3
answered What are examples of two non-similar invertible matrices with same minimal and characteristic polynomial and same dimension of each eigenspace?
Nov
5
comment $AM=I$, where $M$ is a rectangular matrix with full column rank, prove that $A=M^+$?
If that's the case, then the statement in your question is incorrect. The Moore-Penrose pseudoinverse is uniquely defined, whereas $A$ is just a left-inverse of $M$. One-sided inverses of matrices are not unique; there are multiple matrices which can play the role of $A$.
Nov
5
comment $AM=I$, where $M$ is a rectangular matrix with full column rank, prove that $A=M^+$?
What is $M^{+}$? The pseudo-inverse?
Nov
4
comment Concyclic points on a regular polygon
Is $n$ (the number of sides of the polygon) fixed or free? That is, given some number $k$ of concyclic points, are we considering if they lie on a regular $n$-gon for some fixed $n$, or if they lie on a regular $n$-gon for some arbitrary $n$?
Nov
4
comment Concyclic points on a regular polygon
What do you mean by "cyclic points"? I assume that by cyclic you mean concyclic, i.e. that all of the points lie on some common circle.
Oct
30
awarded  Notable Question
Oct
28
comment Two surfaces are not isometries of each other, but have the same Gaussian Curvature
I've rolled back your question to its previous form. Your question already has an answer posted. Please do not change the question completely as that would put the answer completely out of context. Feel free to ask a separate question.
Oct
28
revised Two surfaces are not isometries of each other, but have the same Gaussian Curvature
rolled back to a previous revision
Oct
25
comment Simultaneously Diagonalizable Proof
@Nasser Well, we're looking at the simultaneous diagonalizability of two commuting matrices. If one of the matrices is not diagonalizable, then certainly it cannot be simultaneously diagonazable with another matrix. The assumption that $A$ and $B$ are diagonalizable is within the statement "Therefore, for any eigenbasis of $B$ that we take, the corresponding vectors also form an eigenbasis of $A$." The existence of the eigenbasis is equivalent to $A$ and $B$ being diagonalizable.
Oct
25
comment Simultaneously Diagonalizable Proof
@nasser Indeed I have not. I explicitly stated before that we are considering the case where the eigenspace is one dimensional. My statement follows from that assumption. This is only meant to be a rough sketch and not a rigorous proof.
Oct
23
comment Is there something called the Reduced Column echleon form?
@TheArtist For the purposes of finding rank, you can use any combination of row or column operations you want. You can do row reduction, then do column, then switch back to row, or whatever you want.
Oct
23
comment Is there something called the Reduced Column echleon form?
This is not strictly true. Elementary row and column operations both work for finding rank, but that's only because rank does not change under transpose. For other purposes, such as finding the kernel for example, elementary column operations are not interchangeable with elementary row operations.
Oct
23
answered Is there something called the Reduced Column echleon form?
Oct
8
comment Triangle inequality for subtraction?
@SPRajagopal The only property we used in the proof was the triangle inequality itself, so this holds with any norm.
Sep
30
awarded  Explainer