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$AB-BA=I$ having no solutions - Mathematics Stack Exchange The following question is from Artin's Algebra If A A and B B are two square matrices with real entries, show that AB − BA = I A B − B A = I has no solutions I have no idea on how to tackle this question I tried block multiplication, but it didn't appear to work
$A^2=AB+BA$. Prove that $\\det(AB-BA)=0$ - Mathematics Stack Exchange 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
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,
Find a generating function for the number of strings The string AAABBAAABB is a string of ten letters, each of which is A or B, that does include the consecutive letters ABBA Determine, with justification, the total number of strings of ten letters, each of which is A or B, that do not include the consecutive letters ABBA The conventional way of using casework is too simply and gives the right answer indeed but I am interested in getting the
How to show that - Mathematics Stack Exchange Let A A and B 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 (Is the above result true for matrices with real entries?)
linear algebra - Solving $AB+BA=XBX$ - Mathematics Stack Exchange As it stands, the equation is solvable if and only if A A is a positive scalar matrix Since AB + BA = XBXT A B + B A = X B X T for all positive definite matrices B B, if we pass B B to a limit, the equation is still satisfied when B B is positive semidefinite In particular, AuuT + uuTA = (Xu)(Xu)T A u u T + u u T A = (X u) (X u) T for every nonzero vector u u Since the rank of the RHS is at
Design a Deterministic Finite Automata (DFA) for abab Problem Design a deterministic finite automata (dfa) that satisfies the following: { w | w has 'abab' as a substring} Hence, w can be ε, abab, abababab, etc Attempt This was my first trial It cr