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bio website math.ubc.ca/~israel
location Richmond, Canada
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visits member for 3 years, 6 months
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I'm an Emeritus Associate Professor of Mathematics at University of British Columbia and an Optimization Algorithms Researcher at D-Wave Systems in Burnaby BC


22h
comment Matrix norm square properties.
Obviously you can't take just any $\alpha$ and $\beta$. Quantifiers are important!
22h
comment Matrix norm square properties.
Hint: It wouldn't be true if you required $0 < \alpha$.
22h
comment Solve Identity about Combination
Just expand these out and solve two equations for the coefficients of $n$ and $n^2$.
22h
answered Is the limit point of this sequence unique?
1d
answered Closed Form of Recursion
1d
comment Strategy In auction bidding
You still haven't addressed the problem. Let's take a simple situation. Suppose you know for sure that a bid of $x$ will get you the last lot, and nothing lower will. You can either take it or leave it. What do you do? Presumably there is some maximum $x$ that you would be willing to spend. But you haven't told us what this is.
2d
comment Strategy In auction bidding
The two parts of your objective are in conflict. At the lowest possible price, the probability of acquiring a lot is nearly $0$. If you bid more, you will increase the probability of acquiring one, but it will not be at the lowest possible price. There is a tradeoff. You have not given us any information that might allow us to resolve this.
2d
answered Strategy In auction bidding
2d
comment Are primitive row stochastic matrices diagonalizable?
Try $$\pmatrix{1/2 & 1/2 & 0 & 0\cr 0 & 0 & 1/2 & 1/2\cr 1/2 & 0 & 0 & 1/2\cr 0 & 1/2 & 1/2 & 0\cr}$$ where eigenvalue $0$ has algebraic multiplicity $2$ and geometric multiplicity $1$.
2d
comment Are primitive row stochastic matrices diagonalizable?
The basic methodology was to select the basic form of the matrix subject to parameters, and adjust the parameters to make the characteristic polynomial have discriminant $0$.
Sep
19
answered Are primitive row stochastic matrices diagonalizable?
Sep
19
comment If A is a matrix, what does A' mean?
Transpose, not transposition.
Sep
19
answered Principal branch of the complex logarithm does not always satisfy the product formula
Sep
19
answered Is this log identity true?
Sep
19
answered What is the closed form of $\sum _{n=1}^{\infty }{\frac { {{\rm J_{0}}\left(2\,n\right)} ^{2}}{{n}^{2}}}$?
Sep
18
comment What is the closed form of $\sum _{n=1}^{\infty }{\frac { {{\rm J_{0}}\left(2\,n\right)} ^{2}}{{n}^{2}}}$?
That's not a closed form, it's a numerical approximation.
Sep
18
answered Quadratic forms — rank of matrix
Sep
18
answered Differential equation system changing the eigen-values
Sep
18
comment What does the Fundamental Theorem of Algebra say about…
That's what I said (counting multiplicity). If you count only distinct zeros, then no. For example, $x^2$ has degree $2$ and only one zero.
Sep
18
revised Random variable $X^2$ determined by moments
deleted 1 character in body