AI Tutor
Back to Finding orthogonal bases

Exercise 7

Avg difficulty 2.5

Suppose we have the QRQR factorization A=QRA=QR, where AA is a 7×47\times 4 matrix.

  1. What is the shape of the product QQTQQ^T? Explain the significance of this product.

  2. What is the shape of the product QTQQ^TQ? Explain the significance of this product.

  3. What is the shape of the matrix RR?

  4. If RR is a diagonal matrix, what can you say about the columns of AA?

Austin, Understanding Linear Algebra, §6.4 Finding orthogonal bases, Exercise 7

AI Tutor

Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.