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Thank you for your enlightenment and patience, and for giving me the best memory in my life.


1d
awarded  Popular Question
Jul
6
asked Must the weight function be nonnegative for the greedy algorithm to be optimal for both a matroid and a greedoid?
Jul
5
accepted Is the determinant of a matrix some kind of “integral” of the linear mapping?
Jul
5
accepted Matrices with the same characteristic polynomial
Jul
4
comment Meaning of the characteristic polynomial of a matroid
@JMac31: thanks. What is the usage of characteristic polynomial of a matroid? WHat does it mean?
Jul
4
comment Meaning of the characteristic polynomial of a matroid
Thanks. I mean "how far away".
Jul
4
revised Meaning of the characteristic polynomial of a matroid
added 5 characters in body
Jul
4
asked Meaning of the characteristic polynomial of a matroid
Jul
4
asked What are a geometric system and a finite geometry?
Jul
4
awarded  Nice Question
Jul
4
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@AlgebraicPavel: but as an "integral" of the linear mapping?
Jul
4
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tunococ: Can you write a trace for matrix explictly as some integral? –
Jul
4
comment Matrices with the same characteristic polynomial
@DavidButlerUofA: Then if the multiplicities are not all 1, what can we say about the matrices sharing the same characteristic polynoimal?
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@DanielRust: thanks. can you write it more like an "integral" of the linear mapping $T_A$?
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tunococ: no, that means nothing particular to determinant. I think Daniel Rust might be on one of the right tracks.
Jul
3
comment Matrices with the same characteristic polynomial
(2)if the multiplicities are not all 1, what can we say about the matrices sharing the same characteristic polynoimal? Other than they having the same eigenvalues, eigenspaces?
Jul
3
comment Matrices with the same characteristic polynomial
Thanks. (1) Why is the characteristic polynomial for a matrix called "characteristic", if there can be multiple matrices sharing the same characteristic polynomial? Compared to probability, in probability, we also have a characteristic function for a probability distribution, and different distributions have different characteristic functions, so a characteristic function does characterize a distribution.
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@DanielRust: thanks. can you write "the volume of the image of a unit cube under the corresponding linear transformation" as an "integral"?
Jul
3
comment Matrices with the same characteristic polynomial
@GitGud: What is your definition of characteristic polynomial, if you think it must be monic?
Jul
3
comment Is the determinant of a matrix some kind of “integral” of the linear mapping?
@Tunococ: some kind of "integral", for example, of the corresponding linear mapping to the matrix?