This makes sense. Then it makes me wonder, since you can't assume WLOG that the first component is 1, how do we argue that there are n-1 DOF rather than n?
What about this simpler case: we want to solve for x\in\mathbb{R}^9 and to do so we collect constraints a_i^Tx=b_i. If we can find 9 of...
Hi, if I were you I'd encode all attributes as integers, so that all records can be stored as rows in a matrix of type int. I'll assume that you've done this, and your database is a matrix "db" of size [numusers 4]. I'll let you work out the details of that. First, let me give names to the...
Suppose that for some application it is mathematically convenient to represent certain objects of interest (e.g., lines or conics) as n-dimensional vectors. That such a representation exists lets us conclude that in order to specify such an object, no more than n values are necessary. That is...
I've run into these formulas many times but I've never seen how they were derived.
Say you want to fit a line to some data. Your data is a bunch of (xi,yi) pairs.
Through some kind of magic, the slope m and the y-intercept b are given by these formulas...
Here's the page: http://mathworld.wolfram.com/Hyperplane.html
They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?
This is something that's bothered me for a very long time....
Say you're doing Gaussian elimination on some matrix.
Now suppose during the process, some row gets zeroed out, say row j. Now it makes perfect sense for me to say that row j was a linear combination of the previous rows.
But...
Ok I see. I forgot that E[...] is kind of like the average of many repetitions. I see what you guys are saying, it makes sense that the average of a bunch of positive numbers is positive. Thanks :)
Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect:
1) The variance is the expected difference from the mean...
This is driving me completely crazy!!
QUESTION 1: There are two interpretations I find for the exponential distribution:
1) It models the lifetime of something that does not age in the sense that the probability of functioning yet another time unit does not depend on its current age. So...
Thanks for the replies everyone, but I'm still kind of confused as usual... Forget my first post and tell me what you think of this:
Which sentence in that reasoning is wrong?
If there was only one pair of each (2 light, 2 dark) and the first two were the two lights then the is no third light sock so the probability would be 0..? Hmm I don't really see what you're getting at, sorry...
How is this probability reasoning wrong??
Homework Statement
Homework Equations
The professor didn't say it explicitly, but I'm pretty sure that sock choices are taken to be independent, so P(A,B,C) = P(A)P(B)P(C).
The Attempt at a Solution
The last part is easy...the correct...
I'm not a math or physics guru like these guys so I can't really speak from experience, but I've run into some articles on the Web talking about all the linear algebra that Google uses that I think you might like. Here they are:
How Google Finds Your Needle in the Web's Haystack
The...
This is a great book. It isn't filled with tons and tons of problems (it's not a textbook) but it's still very good. It really cuts through the wordy BS and gets to the heart of things.
Remember that if you really can't afford too many books you could very likely find this one at a library...
I remember reading an interview in a newspaper with a mathematician who I think won the Fields Medal and finding one of his comments really interesting. He said that studying math is actually very ethical, as studying math doesn't pollute the environment, doesn't use natural resources, and...
I like to take notes because I like looking back on them to reminisce about all I've been through. I still have my notes from so long ago when I first got to college, when I took my first calculus course, when I took my first philosophy course, etc. It's a lot of fun looking through them and it...
I just transferred from a CC in California to a UC school, so I'll say a few things. Don't go for an associates. It won't help you transfer. Also, DON'T talk to your CC's counselors for advice on transferring to a UC school for a math-oriented major (math, CS, physics, etc.). They will give you...
I would suggest getting yourself a Nintendo DS and buying Brain Age. Here's a picture Brain Age's calculation game: http://image.com.com/gamespot/images/2006/128/931667_20060509_screen001.jpg [Broken]. The game is a lot of fun and it'll help you at the same time.
Thanks for the inciteful comments everyone.
I'm going to try and stick it out with CS for a little while longer and see how things go, and continue thinking this over. The double major sounds like a great idea, but I don't think it's going to happen. I think it would be cool if I could maybe...
I'm taking an introductory physics course at my university right now.
Let me say something about myself: I *hate* memorizing things. I do anything I can to avoid it. I've held on strong to this viewpoint for years but this physics class is starting to change my mind.
I've spent the...
I'm sort of in a bad dilemma right now and need some advice. I'm a CS major and I've slowly grown to like math more and more and coding and the usual CS stuff less and less. In short, math has become my new passion and I'm thinking of changing my major even though I'm 2.5 years into my CS degree...
This is driving me nuts:
How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.
I'm pretty dumb...I've got a few more questions. My brain doesn't handle matrices very well..
I see your point gonzo how the determinant must be 0 when the columns are dependent. So in other words I can see that dependent columns imply a zero determinant. But....how can I show that a zero...
Well, again I've run into another issue... I'm running into a lot of problems where I'm required to find if some vectors are independent and often the criteria I see used for solving the problem is taking a determinant.
It's said that if you make a matrix out some vectors and find that the...
My teacher gave us an intuitive idea of what it means for two vectors in \mathbb{R}^2 to be linearly independent (they aren't multiples of each other) and for three vectors in \mathbb{R}^3 (they aren't on the same plane).
Now the book has generalized the idea of linear independence to n...
Telling if three vectors in the same plane?? Help!
Hey guys I've got a question about vectors that's confusing me. Here's what my book says:
I don't understand the example... How do you tell if three vectors in R3 are in the same plane? Why does adding the first two and getting (1,1,1) show...
Animals such as tigers and owls are intelligent, living things like you and I and thus some would argue that to kill them unnecessarily is evil. It would follow that if your people had a part in almost annihilating that animal's entire species then it would only be right to at least make an...