Question

Let A be an n × n matrix, v a column vector, and suppose {v, Av,...

Let A be an n × n matrix, v a column vector, and suppose {v, Av, . . . , An−1v} is linearly independent. Prove that if B is any matrix that commutes with A, then B is a polynomial in A.

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 V be a vector space: d) Suppose that V is finite-dimensional, and let S be...
Let V be a vector space: d) Suppose that V is finite-dimensional, and let S be a set of inner products on V that is (when viewed as a subset of B(V)) linearly independent. Prove that S must be finite e) Exhibit an infinite linearly independent set of inner products on R(x), the vector space of all polynomials with real coefficients.
Suppose V is a vector space over F, dim V = n, let T be a...
Suppose V is a vector space over F, dim V = n, let T be a linear transformation on V. 1. If T has an irreducible characterisctic polynomial over F, prove that {0} and V are the only T-invariant subspaces of V. 2. If the characteristic polynomial of T = g(t) h(t) for some polynomials g(t) and h(t) of degree < n , prove that V has a T-invariant subspace W such that 0 < dim W < n
Let V be a vector space of dimension n > 0, show that (a) Any set...
Let V be a vector space of dimension n > 0, show that (a) Any set of n linearly independent vectors in V forms a basis. (b) Any set of n vectors that span V forms a basis.
Suppose we have a vector space V of dimension n. Let R be a linearly independent...
Suppose we have a vector space V of dimension n. Let R be a linearly independent set with order n−2. Let S be a spanning set with order n+ 2. Outline a strategy to extend R to a basis for V. Outline a strategy to pare down S to a basis for V .
Let T be a 1-1 linear transformation from a vector space V to a vector space...
Let T be a 1-1 linear transformation from a vector space V to a vector space W. If the vectors u, v and w are linearly independent in V, prove that T(u), T(v), T(w) are linearly independent in W
Let y ∼ MV N(µ, V ) be a n × 1 random vector and suppose...
Let y ∼ MV N(µ, V ) be a n × 1 random vector and suppose V is nonsingular. Find A and b such that Ay + b is an n-length vector of independent standard normals. Please use Linear Algebra method
Let A be an n by n matrix. Prove that if the linear transformation L_A from...
Let A be an n by n matrix. Prove that if the linear transformation L_A from F^n to F^n defined by L_A(v)=Av is invertible then A is invertible.
Let u, vand w be linearly dependent vectors in a vector space V. Prove that for...
Let u, vand w be linearly dependent vectors in a vector space V. Prove that for any vector z in V whatsoever, the vectors u, v, w and z are linearly dependent.
Let S={u,v,w}S={u,v,w} be a linearly independent set in a vector space V. Prove that the set...
Let S={u,v,w}S={u,v,w} be a linearly independent set in a vector space V. Prove that the set S′={3u−w,v+w,−2w}S′={3u−w,v+w,−2w} is also a linearly independent set in V.
Let V and W be finite-dimensional vector spaces over F, and let φ : V →...
Let V and W be finite-dimensional vector spaces over F, and let φ : V → W be a linear transformation. Let dim(ker(φ)) = k, dim(V ) = n, and 0 < k < n. A basis of ker(φ), {v1, . . . , vk}, can be extended to a basis of V , {v1, . . . , vk, vk+1, . . . , vn}, for some vectors vk+1, . . . , vn ∈ V . Prove that...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT