11 | abba, where a and b are the digits in a 4 digit number.
Nov 21, 2013 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
matrices - When will $AB=BA$? - Mathematics Stack Exchange
Aug 29, 2013 · For example, if A = cI where I is the identity matrix, then AB = BA for all matrices B. In fact, the converse is true: If A is an n × n matrix such that AB = BA for all n × n matrices B, then A = cI for some constant c. Therefore, if A is not in the form of cI, there must be some matrix B such that AB ≠ BA. Share.
Proofs of determinants of block matrices [duplicate]
I know that there are three important results when taking the Determinants of Block matrices $$\\begin{align}\\det \\begin{bmatrix} A & B \\\\ 0 & D \\end ...
How to prove $\\operatorname{Tr}(AB) = \\operatorname{Tr}(BA)$?
Jan 11, 2015 · The efficient @hjhjhj57: answer $$\text{Tr}(AB) = \text{Tr}(BA)= \sum a_{ij} b_{ji}$$ Now we can start to understand why if we do a circular permutation of the factors the expression
The commutator of two matrices - Mathematics Stack Exchange
Viewed 16k times. 1. The commutator [X, Y] of two matrices is defined by the equation. [X, Y] = XY − YX. [X, Y] = X Y − Y X. Two anti-commuting matrices A and B satisfy. A2 = I B2 = I [A, B] = 2iC. A 2 = I B 2 = I [A, B] = 2 i C. (a) Prove that C2 = I C 2 = I and that [B, C] = 2iA [B, C] = 2 i A.
linear algebra - Prove $ (a+ba)^*ba = (a^*ba)^+$ and $ (a+b …
Jun 1, 2018 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Trace of AB = Trace of BA - Mathematics Stack Exchange
Jun 6, 2015 · 3 Answers. by definition trace(AB) = (AB)11 + (AB)22 + ⋯ + (AB)nn = a11b11 + a12b21 + ⋯ + a1kbk1 + a21b12 + a22b22 + ⋯ + a2kbk2 + ⋮ + an1b1n + an2b2n + ⋯ + ankbkn if you view the sum according to the columns, then you see that it is the trace(BA). therefore, trace(AB) = trace(BA).
linear algebra - How to show that $\det(AB) =\det(A) \det(B ...
The determinant changes sign when two rows are exchanged. The determinant depends linearly on the first row. Now we sketch the proof of det (AB) = det (A) det (B). Assume that A and B are nonsingular, otherwise AB is singular, and the equation det (AB) = det (A) det (B) is easily verified.
round table seating probability - Mathematics Stack Exchange
Oct 10, 2014 · To do this, treat the group of a a, b b, and c c as one person, and count the number of arrangements of the four people as. 4! 4 = 6 4! 4 = 6. Your final probability is the number of "successes" (a a has b b to the left and c c to the right) divided by the total number of possibilities, or. 6 120 = 1 20 = 0.05 6 120 = 1 20 = 0.05.
Context free grammar for language { {a,b}*: where the number of …
Mar 28, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.