Hi Chiro,
Thanks a lot for your reply. Okey, I think I understand.
I was figuring maybe it could be possible to achieve something if I did (which you basically was suggesting as well)
C_1AC_2 = B
and then try to find C1 and C2. But having A and B known and C1 and C2 unknown, i.e. two...
I have two known square matrices A and B of different order. Is there any way of constructing a transformation - e.g. a transformation matrix C - that transforms A to B? And, in that case, how do I determine C? Would it be something like this?
AC = B
Or maybe more general, how to determine...
Correction
I looked through this again, and realized that I was wrong about the condition I gave that the rowsums are less than 1. Fortunately, this doesn't have any implications for the proof above, since it just makes use of that the column sums are less than 1. So the proof still holds...
I found something else https://www.physicsforums.com/showthread.php?t=215627". If I make my vector \boldsymbol{a} into a diagonal matrix, it seems that elementwise multiplication would come out if I do
\operatorname{diag}(\boldsymbol{a}) \boldsymbol{b}.
Also found something about the...
Okey, I think I understand now, sort of.
No, I'm actually not adding those values, I'm looking at them separately, as I am interested in the individual output for all the separate industries, not the sum of the output from all the industries. I would loose information if I did sum them up. If...
Hm... I'm still a beginner in linear algebra. What would you say is the whole point with defining vectors and matrices then?
I found it pretty common when you deal with different dataseries, that you would like to do elementwise multiplication. For instance, you could have a vector describing...
How do you mean "up front"? You mean that I explain this in the surrounding text? Okey, that's a possibility, but shouldn't there be a way to express this mathematically?
I was figuring that if you can denote a matrix A=(a_{ij}), which I seen in several texts, then it ought to be possible to...
Hi,
I wonder if anyone knows of a mathematically established way of writing elementwise multiplication between two vectors? In MATLAB you can write A .* B to indicate that you want to multiply the vectors A and B elementwise. In my case, I have two column vectors, A and B, and I want to...
Hi abiyo!
That's a really interesting question! I've been thinking about that for quite a while as well. Why is the matrix multiplication done in the manner it is done? I mean, if we have matrices A and B and multiply AB, why do we take the columns in B and multiply with the rows in A, why not...
Thanks a lot for this derivation, it was really a nifty one! Just a minor thing, I think the rightmost inequality in the uppermost equation above should say "= ||B||a" not "<||B||a", since you already defined a to be the largest column sum of A, with a<1.
I actually found, just the other day...
Hm, that was interesting! Could you explain more in detail how your equation above imply that all the components of An+1 go to zero when n goes to infty? Where exactly in the equation above does one see that? It was a couple of years ago I took my classes in linear algebra... :blushing:
(Edit...
Did you take into account that my assumption wasn't just that |a_{ij}|<1 (actually 0 \leq a_{ij}<1), but also that the row sums and column sums are, one by one, less than 1? In a way, the latter thing seems to imply that |a_{ij}|<1/m, "on the average" at least.
I'll take a look at the...