Bill Cook
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 Feb 2 answered Why are vectors considered to be rank (0,1) tensors and dual vectors considered to be rank (1,0) tensors? Jan 16 answered A improper integral Jan 16 revised A improper integral added 7 characters in body Jan 13 answered Conjugacy classes, irreducible representations, character table of $D_{10}$ (order 20) Jan 7 comment Sums of digits of prime numbers: reference request Nope. i in I indexes the i-th digit. Without digit a_0 you have divisibility by q Jan 7 comment Sums of digits of prime numbers: reference request If you choose your index set $I$ such that $0 \not\in I$, then the number would necessarily be divisible by $q$. For example: $i=\{1,2,3\}$. Then $p=a_1q+a_2q^2=a_3q^3=q(a_1+a_2q+a_3q^2)$. So for any $s >1$, we get a non-trivial multiple of $q$ and $p$ cannot be prime. Jan 7 comment Show a property of a vector space axiom equivalent to another property If you are asked to prove one axiom is equivalent to some other statement, you need to be very careful which lemmas you use. You don't want to end up assuming what you're proving. In your case, showing that the existence of inverses implies that $0v=0$, using that lemma is fine. On the other hand, showing that $0v=0$ implies the existence of inverses, using the lemma probably isn't ok unless that lemma is proven without assuming the inverse axiom (which I'm betting it does). In the end, if you are asked to prove one axiom is equivalent to another, the safest route is to avoid using an lemmas. Jan 7 comment Show a property of a vector space axiom equivalent to another property This proof suffers from the same problems as the proof posted by the OP. Namely, you've assumed $-1v=-v$ (which is true). However, $-1v=-v$ is not an axiom. It needs to be proven. Jan 7 answered Show a property of a vector space axiom equivalent to another property Jan 6 answered Basic understanding of quotients of “things”? Jan 6 answered euclidean norm expressed as a supremum Dec 17 answered Show the Jacobian back to itself is 1 Dec 10 answered Cycle type of elements in left regular presentation Dec 8 revised Eigenvalues of two matrices associated to the same endomorophism are different? added 1170 characters in body Dec 8 answered Eigenvalues of two matrices associated to the same endomorophism are different? Nov 30 answered Quotient Space Notation Nov 11 comment Comparing cardinality of sets Sure, no problem. Counting problems always leave me a little uneasy -- it's so easy to miss a case or double count something. It's nice to have a solid formula to hang your hat on. :) Nov 11 answered Comparing cardinality of sets Nov 4 comment Determine the Type and the General Solution of an ODE sosmath.com/diffeq/first/lineareq/lineareq.html Nov 3 comment Use group homomorphism to prove that for systems of linear equations, general=particular+homogeneous If y is a vector of functions as well as g and if A is a matrix of functions, this is essentially the definition of a (non homogeneous) linear system.