Thank you guys, I think I understand it now.
I have a different, but related question, and I'll ask it here so as to avoid clogging up the forum with another dual space question.
After wrestling with it for a while, I think I have a comfortable, intuitive sense of how and why a dual...
I'm in a Second Course in Linear Algebra this semester, and we've just been introduced to the idea of a dual space, dual vectors and briefly to a double dual space. I completely understand how all of these things work and how they're defined, but I don't understand why we care.
I've been...
This is a ridiculously easy question, so I apologize for bugging you all with it, but google has been less than helpful.
Consistently when I watch videos of rocket launches I hear operators talking about propellant utilization being active (usually with individual stages singled out). What does...
I see that, and many people (including me after I'd left the test) did it that way or thought about doing it that way.
I still don't quite see why a and b aren't symmetric though? Where is the asymmetry?
I just got back a test and I received 0 for the following problem. I am (somewhat) comfortable with the idea that my justification isn't good enough, but I'm a little unsure where my error is so I would love to have someone illuminate that for me.
The problem was to show that the gcd(a,b) =...
Well what else do you want?
I can say for constant velocity that Velocity is proportional to distance traveled and inversely proportionally to time elapsed.....but I'm really saying the exact same thing as ##V=\frac{s}{t}##; just in a different way.
I don't like the term dependent variable vs independent variable. I prefer to say that "y is a function of x" or vice versa; meaning that if y is a function of x then it can be put into the form y=f(x).
Remember that an ellipse is not a function; it doesn't pass the vertical line rule (in my...
True, in fact there is a procedure in my linear algebra textbook precisely identical to this. But in practical usage, you're going to end up row reducing as described by HallsofIvy if you want to find a basis for a less-trivial set of vectors.
Hi all,
I'm testing out a matrix solving program and while it checks out for 2x2/3x3/4x4 I would like to try it out on some larger matrices, but I don't really want to go through the hassle of row reducing a couple of 10x10 matrices to double check my program.
Does anyone happen to know of...
In spreadsheet programs like excel this is done by putting '$' '$' around the variable, though I doubt that's what you're looking for.
Do you mean just saying:
##D= \frac{v}{t} \rightarrow D= \frac{v_1}{t}##? Because that sort of does it.
You may be :P
Totally agree with this, it turns out that if you look at the average velocity over two points and you keep making the points closer to each other, the average velocity keeps getting closer and closer to a specific number. If you make the points infinitely close, the average...
Velocity is defined as ##\frac{\Delta Displacement}{\Delta Time}## or ##\frac{dx}{dt}## or any one of probably dozens of equivalent definitions. What are you looking for?
Thank you so much. The reason I didn't set those to values (and I had done that several other times throughout my code) is that I had mistakenly thought that doing so implicitly set the value at zero, likewise I had forgotten about the =/== distinction, so thank you.
The reason I am comparing...
Sorry for the triple post in advance.
I had finished both the matrix entry, storage and printing, and had built my transpose function. I soon realized that the way my matrix print function worked (printed numbers in sequential order from their array) wasn't going to let my transpose function...
Hey, sorry to bother you guys again.
Work's coming along steadily on this next incarnation (and a hell of a lot cleaner). But could one of you explain how I should go about passing arrays to functions (or how I achieve this affect; I've come to understand functions cannot take arrays as...
Because when you take a line integral from (0,0) to (0,3) in a density field z = f(x,y) you're not just finding out what the mass of a 3 cm wire is you're finding out what the mass of a 3 cm wire is when density is defined by z = f(x,y).
In your mind you're thinking that the 3 cm wire already...
f(x,y) gives you a value of density for all points in the x-y plane. Taking a line integral through that plane is like 'cutting out' a wire from that density plane.
Unless f(x,y) is constant, there is no reason to assume that one wire cut out would be the same density as another.
I think what...
I'm just figuring that out.
I rewrote the whole thing in 2-D Arrays but I just got frustrated enough to close it for the night.
I'm planning on re-writing it again tomorrow or the next day using 1-D arrays but in a nicer style/one that would be able to be expanded on easier.
Thanks for...
To Mark, makes sense. It was indented differently before I posted I added indents for increased clarity, but I definitely prefer what you were doing to mine!
By the way I had forgotten to post here earlier, Aleph you nailed it so thank you! It was really interesting it consistently worked up...
Hello all,
I'm not really a programmer at all, but I learned c++ for a while so I can do basic stuff. Having just finished my linear algebra class I suddenly had an urge to write myself a simple matrix solver. I knew it wouldn't be easy (especially because of my lack of skill) but I was...
Well, firstly, the range of the dr-integral should be 0 to 9 not 0 to 9 because we're dealing with the cylinder of radius 9, not the equation x^2+y^2 <= 9.
But that won't affect the problem, I just did this myself and I also got 0. Unless someone else can point out a mistake we both made, I...
Huh, you know I've known about tensors for a while but in a purely pop-science way (the only actual tensors I've been exposed to were in a five-minute digression by my teacher briefly explaining them), I hadn't ever been told to think of them that way!
Well, I guess its a scientist's joke. The idea is that if something appears that wasn't there before, a physicist is used to calling this a measurement error, a biologist is used to observing unexpected reproduction and a mathematician doesn't care about the real world, just about the pure math...
I just had my last Linear Algebra class, and I didn't get a chance to ask the one question that has been bugging me ever since we started in earnest with matrices.
Why aren't there cube matrices? I mean, mathematical entities where numbers are 'laid out' in 3d not in 2d (not quite...
No.
##
\left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] = I##
So ##2I = \left[ \begin{array}{cc} 2 & 0 \\ 0 & 2 \end{array} \right]##
Really, I should be saying ##I_n## (##I_2## in this case), but generally the dimension of the identity matrix is suppressed and you make it as big...
There was a paper published I want to say about a year ago (I looked but could not find it) that was somewhat along these lines. I could only get a little way through it because it was technical but the gist was that the paper was exploring what superluminal travel would be like according to...