48,365 reputation
337100
bio website www-math.univ-poitiers.fr/…
location Poitiers, France
age 54
visits member for 2 years, 11 months
seen 6 mins ago

professor of mathematics at the Université de Poitiers (France)


3m
comment Intersection of inverse images
I mean that opening the sentence with "This means" indicates a relation with the previous statement, which is "$x\in f^{-1}(E)$ and $x\in f^{-1}(F)$". So there should be some relation between $y_1,y_2$ and the $x$ of that statement. Write down that relation and you're almost done.
37m
comment If two vectors are orthogonal, linearly independent?
For any vector $x$, the vectors $\vec0$ and $x$ are orthogonal but not linearly independent.
40m
answered Intersection of inverse images
45m
revised Intersection of inverse images
Use a correct term in the title
56m
answered Proof of linear independence of $e^{at}$
2h
answered Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
2h
comment Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
To be honest the "common false belief" linked to is not that a sum of subspaces is direct whenever the sum of every pair of them is direct; anyone doing linear algebra should realise that this is much to weak a hypothesis. The false belief is that a complicated formula holds between dimensions of intersections of subspaces, which tries to mimic the principle of inclusion/exclusion. It happens that this false belief would imply that a sum of pairwise independent subspaces is direct, but those that hold the false belief probably do not realise that (and would cease to believe when they do).
3h
answered Eigenspace, Diagonalizable, Direct Sum
3h
answered Finding the transformation matrix R
3h
revised Show that a set of vectors is linearly dependent
added 1 character in body
3h
answered Show that a set of vectors is linearly dependent
4h
comment Proof of linear independence of $e^{at}$
What is the characteristic polynomial of an element of a vector space (of functions)?
5h
awarded  linear-algebra
11h
revised Help in proving an algebraic identity involving powers of binomials.
added 7 characters in body
11h
answered Help in proving an algebraic identity involving powers of binomials.
13h
comment Question on Showing the dimensions of a Vector Space
When you say $\dim(A)$ (which makes no sense, subspaces have dimensions, matrices do not), you appear to mean $\dim(\ker(A))$.
16h
revised Factorial as a sum. Insight appreciated
edited body
17h
revised Factorial as a sum. Insight appreciated
added 918 characters in body
22h
comment Finding the Integral of a function
IMO such an answer is quite pointless is you do not motivate the choice of substitution. If you need to just learn by rote that "such and such integral can be solved using such and such substitution", then you might as well instead learn by heart their primitives; this would be faster and avoid computational error in applying the substitution.
1d
answered How do I solve this fraction addition problem?