Find the constants m and b in the linear functions f(x)=mx+b such that f(0)=4 and f(3)=-2 What would I do first when using the order of operations to solve (5+3-2*4)/6? What is a vector? Why is 3(x - 3) not a monomial?
As before, every linear inequality or equality that is valid for the information-theoretic quantities discussed above, is automatically valid for the linear algebra counterparts for subspaces of a vector space over a finite field by applying the above specialisation (and dividing out by the normalisin...
This is analogous to how, in undergraduate mathematics and physics, vectors in Euclidean space are often depicted as arrows of a given magnitude and direction, with the initial and final points of this arrow being of secondary importance only. (Indeed, this depiction of vectors in a vector spac...
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in accuracy. What is incredible about Google Translate is what is actually happening inside the computer, in the middle of any translation. In the old days one would translate word for word between say English and French. The problem is that language is a very funny thing and it doesn’t ...
This is a lie — a white lie, but a big one. In fact there are zillions of gluons, antiquarks, and quarks in a proton. The standard shorthand, “the proton is made from two up quarks and one down quark”, is really a statement that the proton has two more up quarks than up ...
I am assuming a university level affair:It is VERY heavy on the math the first couple of years, and real projects are a once in a blue moon thing, you can probably pass the course without ever once touching a soldering iron, never mind a layout package!As memory serves, first year for...
is never zero. (Rolle’s theorem does imply that the real and imaginary parts of the derivative both vanish somewhere, but the problem is that they don’tsimultaneouslyvanish at the same point.) Similar remarks to functions taking values in a finite-dimensional vector space, such as ...
24 May, 2013 in expository, math.GR, math.OA, math.RT | Tags: characters, convolution, Frobenius groups, Frobenius theorem, idempotents | by Terence Tao | 8 comments A finite group is said to be a Frobenius group if there is a non-trivial subgroup of (known as the Frobenius complemen...
Here is the fibring identity: Proposition 5 (Fibring identity) Let be a homomorphism. Then for any independent -valued random variables , one has The proof is of course in the blueprint, but given that it is a central pillar of the argument, I reproduce it here. Proof: Expanding ...