Let {v1, v2, ..., vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A be the n x n matrix with row vectors vị, V2, . . . , Un- a) Show that the matrix AAT is a diagonal matrix.

Let {v1, v2, ..., vn} be an orthogonal set in R" with respect to the Euclidean inner product. Let A be the n x n matrix with row vectors vị, V2, . . . , Un- a) Show that the matrix AAT is a diagonal matrix.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let {v1, v2, . , vn} be an orthogonal set in
R" with respect to the Euclidean inner product. Let A be the n xn
matrix with row vectors vị, V2, . . . , VUn.
a) Show that the matrix AAT is a diagonal matrix.

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