#math - Mon 26 Feb 2007 between 00:00 and 00:19

NY Lost Funds

 Cosmo-san is anyone here knowledgeable with Second Solutions by reduction of order? TRWBW http://www.sosmath.com/diffeq/second/reduction/reduction.html Cosmo-san ah, thank you Phylo % Integrate[x/E^(X), x] mbot Phylo: x^2/(2*E^X) Phylo does case matter for x? excelblue yesthey even matter on paper Phylo indeed it doeslol, trueis there a simpler way other than integration by parts to solve x/E^(x)? JIMJONESBALLIN Suppose that _1 and _2 are two inner product spaces on a vector space V. Prove that = _1 + _2 is also an inner product on V. TRWBW JIMJONESBALLIN: what's the def of an innner product space? just to get it all out in the openJIMJONESBALLIN: um, inner product JIMJONESBALLIN Its a Vector space over a field endowed with an inner product. TRWBW JIMJONESBALLIN: so are you talking an arbitrary field or R or C or what? JIMJONESBALLIN The question doesnt say. But I think its over F^nNo, my apologies. Its over |R TRWBW JIMJONESBALLIN: so is your problem that you don't understand the question?JIMJONESBALLIN: k seb-_ % Solve[a x x + b x + c == 0, x] mbot seb-_: {{x -> (-b - Sqrt[b^2 - 4*a*c])/(2*a)}, {x -> (-b + Sqrt[b^2 - 4*a*c])/(2*a)}} TRWBW JIMJONESBALLIN: is your question how to solve this, or what is the definition of an inner product? JIMJONESBALLIN I'm tryna prove it. TRWBW JIMJONESBALLIN: what are you trying to prove? i'm asking do you know the definition of an inner product? Phylo ... if x and X are different, what is E as opposed to e? |Steve| So show that <-,->_1 + <-,->_2 satisfies the properties of an inner product. JIMJONESBALLIN Oh sorry, I thought you asked for the definition of an inner product space. Phylo and why doesn't e^f(x) work? TRWBW |Steve|: i'm trying to get at that. is his problem how to show it, or that he doesn't know what the definitions involved are? Phylo where E^f(x) does JIMJONESBALLIN An inner product on a vs V is just a function that assigns to every ordered pair of vectors x and y in V a scalar in F denoted |Steve| Phylo: That was already answered. e is a variable, E is the base of the natural logarithm. TRWBW JIMJONESBALLIN: just? JIMJONESBALLIN No, more to follow. TRWBW k dn4 [1+2xCos(x)+sin^2(x)]/[x^2+2xCos(x)+Cos^2(x)] <-- when reducing this fraction's "2xCos(x)" Does it = [1+1+sin^2(x)]/[x^2+1+Cos^2(x)] ? |Steve| It's also F-linear in the first argument, etc. TRWBW |Steve|: i'm sure you know it. ;) JIMJONESBALLIN such that for all x,y and z in V and all c in F we have: a) = +