Question: Show that if U is an n x n orthogonal matrix then u1uT1 + u2uT2 + + unuTn = I

Show that if U is an n x n orthogonal matrix then
u1uT1 + u2uT2 +∙ ∙ ∙ ∙+ unuTn = I

Step by Step Solution

★★★★★

3.34 Rating (154 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

I 1 2... View full answer

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

Document Format (1 attachment)

Word file Icon

949-M-L-A-E (736).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Show that if u, v Rn, then det (I + uvt) = 1 + vtu.

Q:

If Q is an n x n orthogonal matrix and x and y are nonzero vectors in Rn, then how does the angle between Qx and Qy compare to the angle between x and y? Prove your answer.

Q:

Show that if U is an n à n unitary matrix and |z1| = |z2| = ... = |zn| = 1, then the product is also unitary. Z1 0 0.0 0 z200 0 0 0 Zn

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

A is an m x n matrix with a singular value decomposition A = UV T , where U is an m x m orthogonal matrix, is an m x n "diagonal" matrix with r positive entries and no negative entries, and V is an...

Q:

1. Partners Allen, Baker, and Coe share profits and losses 50:30:20, respectively. The balance sheet at April 30, 2011, follows: The assets and liabilities are recorded and presented at their...

Q:

Explain the differences in a bank credit card, a premium or prestige credit card, an affinity credit card, and a secured credit card. What are credit card classes?

Q:

Maddie owns an automobile for personal use. The adjusted basis is $ 1 9 , 7 6 0 , and the FMV is $ 1 6 , 1 3 0 . Assume Maddie has owned the automobile for two years. Required: o . Respond to the...

Q:

4. For each of the transactions listed in Test Yourself Question 3, what will be the ultimate effect on the money supply if the required reserve ratio is one-eighth (12.5 percent)? Assume that the...

Q:

In each case, show that the linear transformation T satisfies T2 = T. (a) T: R2 R2; T(x, y) = (x + y, 0) a+e b+d a +e b+d

Q:

Determine whether each of the following transformations T has an inverse and, if so, determine the action of T-1. (a) T: R4 R4; T(x, y, z, t) = (x + y, y + z, z + t, t + x) (b) (c) T: P, R3: T(p) =...

Q:

In each case, show that T is self-inverse: T-l = T. (a) T: R2 R2; T(x, y) = (ky - x, y), k any fixed number 4

Q:

Bermuda Triangle Corporation (BTC) currently has 420,000 shares of stock outstanding that sell for $94 per share. Assuming no market imperfections or tax effects exist, what will the share price be...

Q:

Compute the discounted payback statistic for Project C if the appropriate cost of capital is 8 percent and the maximum allowable discounted payback period is three years. ( Do not round intermediate...

Q:

Savory Seafood Inc.s managers select projects based only on the MIRR criterion. Should Savory Seafood Inc.s managers accept this independent project? Yes or no? 8. Cash flow patterns and the modified...