- Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange
The Problem Let A A be the matrix (a c b d) (a b c d), where no one of a,b,c,d a, b, c, d is 0 0 Let B B be a 2×2 2 × 2 matrix such that AB+ BA= (0 0 0 0) A B + B
- How many ways can we get 2 as and 2 bs from aabb?
If I do this manually, it's clear to me the answer is 6, aabb abab abba baba bbaa baab Which is the same as \mathchoice((((4 2\mathchoice)))) \mathchoice ((((4 2 \mathchoice)))) But I don't really understand why this is true? How is this supposed to be done without brute forcing the question?
- sequences and series - The Perfect Sharing Algorithm (ABBABAAB . . .
The algorithm is normally created by taking AB, then inverting each 2-state 'digit' and sticking it on the end (ABBA) You then take this entire sequence and repeat the process (ABBABAAB)
- How to calculate total combinations for AABB and ABBB sets?
Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB ), where order matters and repetition is allowed, both can be rearranged in different ways: First one: AABB, BBAA,
- $A^2=AB+BA$. Prove that $\\det(AB-BA)=0$
Let A, B A, B be two 3 × 3 3 × 3 matrices with complex entries, such that A2 = AB + BA A 2 = A B + B A Prove that det(AB − BA) = 0 det (A B B A) = 0 Nice problem, and I want to find a solution AB − BA = A2 − 2BA = (A − 2B)A A B B A = A 2 2 B A = (A 2 B) A so if |A| = 0 | A | = 0 we have done, if |A| ≠ 0 | A | ≠ 0 I can't prove
- elementary number theory - Divisibility Tests for Palindromes . . .
The 4 4 -digit palindrome abba a b b a is divisible by 101 iff a = b a = b The 5 5 -digit palindrome abcba a b c b a is divisible by 101 iff c = 2a c = 2 a The 6 6 -digit palindrome abccba a b c c b a is divisible by 101 iff a + b = c a + b = c The 7 7 -digit palindrome abcdcba a b c d c b a is divisible by 101 iff d = 2b d = 2 b
- How many words of length - Mathematics Stack Exchange
{AABB, ABAB, ABBA, BBAA, BAAB, BABA} {A A B B, A B A B, A B B A, B B A A, B A A B, B A B A} So, I need to know what this w(n) = w(ni,nj) w (n) = w (n i, n j) is Some references on aproaches on how to solve this kind of problems and related algorithms to generate such words would be apreciated Thanks
- CW complex for Möbius strip and its homeomorfisams
is attaching a map for ABBA It is easy to see that these maps are continuous And f(x) = x+1 2 f (x) = x + 1 2 for second 1-cell Is this okey? According to this question, there is CW complex with one 0-cell,one 1-cell and one 2-cell I think that o-cell is A, 1-cell is circle ABBA, and 2-cell is Int(M) I n t (M), but I can't find homeomorfism for 2-cell Can someone help? edit: picture on
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