Question: Let V be a finite dimensional C-vector space and T L (V ). If 1 , 2 , ..., m are the distinct eigenvalues of

Let V be a finite dimensional C-vector space and T L (V ). If ₁, ₂, ..., _m are the distinct eigenvalues of T, then prove that T is diagonalizable if and only if the minimal polynomial of T is (t ₁)(t ₂) (t _m)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Figure 23-65 is a photograph of an eyeball with the image of a boy in a doorway. (a) Is the eye here acting as a lens or as a mirror? (b) Is the eye being viewed right side up or is the camera taking...

Let V be a finite dimensional vector space. Suppose that TE L(V) has dimV distinct eigenvalues and that S E L(V) has the same eigenvectors as T (not necessarily the same eigenvalues). Prove that ST =...

Let V be a finite dimensional vector space and consider S,T in End(V). 1. Show that ST is invertible if and only if both S and T are invertible. 2. Prove that ST=I iff TS=I 3. Give an example...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Let V be a finite dimensional vector space over C. Let D, N L(V). Suppose the operator D is diagonalizable, and operator N is nilpotent. Also DN = ND. We are going to let 1,...,m be the distinct...

Explain the following que.stions as attached below. Pages 2-5 Q1 a) Let V be a finite dimensional vector space over a field F. If S and S' are two different bases of V, then prove that the number of...

Please help Adobe Reader Touch X ASSIGNMENT 04 Due date: Thursday, 30 April 2020 UNIQUE ASSIGNMENT NUMBER: 897728 ONLY FOR SEMESTER 1 INSTRUCTIONS FOR THE ASSIGNMENT Take care to explain all your...

6. Let V be a finite dimensional vector space over a field F, and let R. Te C(V). Suppose that S e C(V) is invertible, and that T = SRS-1. Let Kx(T) denote the A-generalized eigensapce of T; and...

Can anyone help me with 6b? 6. Let V be a finite dimensional vector space over a field F, and let R, Te C(V). Suppose that Se C(V) is invertible, and that T = SRS-1. Let Kx(7) denote the...

Suppose V is a finite dimensional vector space and that L: V V is a linear operator that satisfies L(L()) = L(T) for all & EV. (a) Show that A = 0 and X = 1 are the only possibilities for the...

6. Show that there does not exist a lincar transformation T: R5 R5 such that R(T) N(T). 7. Let A be a 5 3 matrix having the null space spanned by the column matrices Find the rank of A. , and 3 8. A...

If a firms earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain Briefly.

When Steve Jobs first demonstrated "the pinch"-the two-finger gesture to zoom in and out on photos and Web pages on the iPhone, it just rocked the mobile phone industry-the whole digital world heard...

Berikut informasi PT. Sandang atas biaya pemeliharaan mesin konveksinya selama tahun 2023: Bulan Jam Mesin Biaya Pemeliharaan Januari 120 2.000.000 Februari 150 2.500.000 Maret 185 2.800.000 April...

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.