Question

Let n be a positive integer and let U be a finite subset of Mn×n(C) which...

Let n be a positive integer and let U be a finite subset of Mn×n(C) which is closed under multiplication of matrices. Show that there exists a matrix A in U satisfying tr(A) ∈ {1,...,n}

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let n be a positive integer and let S be a subset of n+1 elements of...
Let n be a positive integer and let S be a subset of n+1 elements of the set {1,2,3,...,2n}.Show that (a) There exist two elements of S that are relatively prime, and (b) There exist two elements of S, one of which divides the other.
4) Let F be a finite field. Prove that there exists an integer n ≥ 1,...
4) Let F be a finite field. Prove that there exists an integer n ≥ 1, such that n.1F = 0F . Show further that the smallest positive integer with this property is a prime number.
Let A be a 2 × 2 matrix satisfying A^k = 0 for some positive integer...
Let A be a 2 × 2 matrix satisfying A^k = 0 for some positive integer k. Show that A^2 = 0.
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix,...
Let matrices A,B∈Mn×n(R). Show that if A and B are each similar to some diagonal matrix, and also have the same eigenvectors (but not necessarily the same eigenvalues), then  AB=BA.
Let A be a square matrix, A != I, and suppose there exists a positive integer...
Let A be a square matrix, A != I, and suppose there exists a positive integer m such that Am = I. Calculate det(I + A + A2+ ··· + Am-1).
Let n greater than or equal to 1 be a positive integers, and let X1, X2,.....,...
Let n greater than or equal to 1 be a positive integers, and let X1, X2,....., Xn be closed subsets of R. Show that X1 U X2 U ... Xn is also closed.
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar...
Show that the set GLm,n(R) of all mxn matrices with the usual matrix addition and scalar multiplication is a finite dimensional vector space with dim GLm,n(R) = mn. Show that if V and W be finite dimensional vector spaces with dim V = m and dim W = n, B a basis for V and C a basis for W then hom(V,W)-----MatB--->C(-)--------> GLm,n(R) is a bijective linear transformation. Hence or otherwise, obtain dim hom(V,W). Thank you!
Let λ be a positive irrational real number. If n is a positive integer, choose by...
Let λ be a positive irrational real number. If n is a positive integer, choose by the Archimedean Property an integer k such that kλ ≤ n < (k + 1)λ. Let φ(n) = n − kλ. Prove that the set of all φ(n), n > 0, is dense in the interval [0, λ]. (Hint: Examine the proof of the density of the rationals in the reals.)
Let n be a positive integer. Show that every abelian group of order n is cyclic...
Let n be a positive integer. Show that every abelian group of order n is cyclic if and only if n is not divisible by the square of any prime.
The trace of a square n×nn×n matrix A=(aij)A=(aij) is the sum a11+a22+⋯+anna11+a22+⋯+ann of the entries on...
The trace of a square n×nn×n matrix A=(aij)A=(aij) is the sum a11+a22+⋯+anna11+a22+⋯+ann of the entries on its main diagonal. Let VV be the vector space of all 2×22×2 matrices with real entries. Let HH be the set of all 2×22×2 matrices with real entries that have trace 11. Is HH a subspace of the vector space VV? Does HH contain the zero vector of VV? choose H contains the zero vector of V H does not contain the zero vector...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT