Question: Let f be a linear operator on a Euclidean space, and let the matrix A = (aij) represent f with respect to an orthonormal basis.

Let f be a linear operator on a Euclidean space, and let the matrix A = (aij) represent f with respect to an orthonormal basis. Then f is a symmetric operator if and only if A is a symmetric matrix, that is, A = AT.

Step by Step Solution

★★★★★

3.45 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

x x x x x x an... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

914-M-N-A-O (668).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Let L be a linear operator on a vector space V. Define Ln, n 1, recursively by L1 = L Lk+ l(v) = L(Lk(V)) for all v V Show that L" is a linear operator on V for each n > 1.

Let L be a linear operator on a vector space V. Let A be the matrix representing L with respect to the ordered basis [v1,...,vn] of V [i.e., L(j) = Show that A'" is the matrix representing L'" with...

Let L be a linear operator on R1 and let a = L(l). Show that L(x) = ax for all .v R1

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Let the matrix A = (aij) represent a linear operator with respect to an orthonormal basis x1; x2,..., xn for an inner product space X. Then aij = xTf (xj) for every i, j A link between the inner...

Theorem 6.14 (Schur). Let T be a linear operator on a nite- dimensional inner product space V. Suppose that the characteristic poly- nomial of T splits. Then there exists an orthonormal basis 7 for V...

Let the matrix A = (aij) represent a linear operator f with respect to the orthonormal basis x1; x2; . . . ; xn. Then the sum defines a quadratic form on X, where x1; x2; . . . ; xn are the...

9. Let T be a linear operator on a nite-dimensional vector space V, and suppose there exists an ordered basis if for V such that [T] 5 is an upper triangular matrix. (a) Prove that the characteristic...

a State and prove the Cayley Hamilton The b Let T be a linear operator defined on a vector space V F for n Zt Let A be a matrix representation for T with respect to some basis for V i Prove that the...

(3) (25 pts) Let V' = V3 be the vector space of polynomials in a single variable x of degree at most 3 with complex coefficients. Let 7" be the linear operator T(f) = f + f". (a) Compute the...

A firm has a long-term debt to equity ratio of .4. Shareholders' equity is $1 million. Current assets are $200,000 and the current ratio is 2. The only current liabilities are notes payable. What is...

Let f(x, y) on R2, and F is unbounded in R?. Further, show that f(x, y) is coercive on F, i.e., x2 + y, and F = {(x, y) E R2 | x+ y > 1}. Show that f(x, y) is not coercive lim (r,y)EF f(x, y) = 00.

In the case of convertible bonds, what adjustments must be made to the numerator and the denominator in the EPS calculation?

Explain the importance of the rule of law to economic development, and discuss how the government and the market deal with asymmetric information.

Use Fishers LSD method to analyze the mean response times for the three circuits described in Exercise 13-6. Use a = 0.01.

Use Fishers LSD method to analyze the mean amounts of radon released in the experiment described in Exercise 13-8. Use a = 0.05.

Apply Fishers LSD method to the air void experiment described in Exercise 13-9. Using a = 0.05, which treatment means are different?

please answer all 3! QUESTION 1 Eaton Vance Company has sales of $200,000, Cost of Goods Sold of 100,000, a net income of $15,000, and the following balance sheet: Cash $ 10,000 Accounts payable $...

RAK, Inc., has no debt outstanding and a total market value of dollar 240, 000. Earnings before interest and taxes, EBIT, are projected to be dollar 28,000 if economic conditions are normal. If there...

You own a stock portfolio invested 30 percent in Stock Q, 15 percent in Stock R, 5 percent in Stock S, and 50 percent in Stock T. The betas for these four stocks are 1.49, 1.3, 1.05, and 0.93,...