Horn’s inequality for singular values via exterior algebra
\( \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\sgn}{sgn} \DeclareMathOperator{\Id}{Id} \)Horn’s inequality states that for any two compact operato...
Tag: Mathematics
Every continuous open mapping of R into R is monotonic
I’m willing to bet that most students who have used Rudin’s Principles of Mathematical Analysis have encountered this problem: 15. Call a mapping of...
Strictly positive extensions of linear functionals
There is an interesting exercise in Steven Roman’s book Advanced Linear Algebra:
Power series of tan(x), cot(x), csc(x)
Here’s a little how-to on figuring out the power series of tan(x), cot(x) and csc(x). Start with the generating function for the Bernoulli numbers: