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5h
answered Solving a system of ODEs with variable in matrix A
5h
answered Representation of a matrix as product of unitary matrices and diagonal matrix
5h
comment Representation of a matrix as product of unitary matrices and diagonal matrix
Presumably Ram is using a version of "positive semidefinite" that does not require a symmetric (real) or hermitian (complex) matrix. See en.wikipedia.org/wiki/Positive-definite_matrix
5h
answered How can I prove $\phi(m)*\phi(n) = \phi(lcm(m,n))* \phi(\gcd(m,n))$ where $\phi$ is eulers $\phi$ function?
7h
revised Magic square of 5
Entered the matrix in LaTeX
11h
answered Show that f(x) is convex
16h
answered Finite field, how to satisfy equation?
16h
answered Linear Algebra-invariant subspaces
16h
comment Linear Algebra-invariant subspaces
You must assume your vector space, or at least the subspace, is finite-dimensional: there are examples with infinite-dimensional invariant subspaces.
17h
comment Linear Algebra-invariant subspaces
Presumably what is meant is $T \in L(V)$.
17h
comment Conditions for Laplace Transform
Whenever you use Laplace transforms to solve differential equations, an implicit "For $\text{Re}(s)$ sufficiently large" applies to all the calculations. The point is that to recover a continuous function from its Laplace transform, it suffices to know the Laplace transform for $\text{Re}(s)$ greater than some arbitrary real number.
17h
comment How various properties of numbers, operations are found?
At least in the case of commutativity and associativity for positive integers, it's not clear that they were ever "found" per se: even pre-school children will know that the results of taking two apples and then three more apples, or three apples and then two apples, will be the same. You might look at mathforum.org/library/drmath/view/52599.html
17h
revised If each term in a sum converges, does the infinite sum converge too?
added 4 characters in body
17h
revised If each term in a sum converges, does the infinite sum converge too?
added 366 characters in body
17h
answered If each term in a sum converges, does the infinite sum converge too?
17h
answered How to fastest approximate definite integrals
17h
comment How to fastest approximate definite integrals
Mathematica's standard methods for 1D integrals do not use Monte Carlo. They use numerical techniques that are much more accurate for smooth functions. The reference you gave shows how to compute a Monte Carlo approximation in Mathematica and compare the result to a much more accurate value obtained without Monte Carlo.
18h
comment Conditions for Laplace Transform
Actually, if you allow complex numbers, the integral converges for $\text{Re}(s) > 0$. But what do you mean by "how do we know that this condition is satisfied"? The Laplace transform of a function is a function of a new variable $s$. Like any variable, it has whatever value you give it. If you want $s > 0$, make sure you only ever give it values $> 0$.
18h
answered finding the value of a node in Pascal’s (a.k.a Yanghui's) triangle
18h
comment Unilateral Z-Transform of sen($\frac{\pi}{4}n$)
By $\text{sen}$ do you mean $\sin$? If so, write in terms of complex exponentials and you get geometric series.