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Chapter 5: Q23E (page 263)

The entries of an orthogonal matrix are all less than or equal to 1.

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Step by step solution

01

Step by step solution Step 1: Definition of an orthogonal matrix

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix.

Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

02

Determine whether the statement is true or false

For example,

Suppose A is a square matrix with real elements and of n x norder and ATis the transpose of A. Then according to the definition, ifAT=A-1 is satisfied, then,

AAT=I

Since, the columns vectors are the unit vectors.

Hence, the statement is true.

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Most popular questions from this chapter

Prove Theorem 5.1.8d.(V鈯�)鈯�=Vfor any subspaceV of鈩�n.

If the nxnmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well? AT.

If the nxn matrices Aand Bare symmetric and Bis invertible, which of the matrices in Exercise 13 through 20 must be symmetric as well? 3A.

Using paper and pencil, find the QR factorization of the matrices in Exercises 15 through 28. Compare with Exercises 1 through 14.

19.[212115]

Is there an orthogonal transformation T from R3to R3such thatT[230]=[302]

and T[230]=[302]?
See all solutions

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