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There are several other ways to express the vector of residuals e that will prove useful, including: e = y-y=y-Xß = y - Hy = (I −H)y Prove that the matrix H and I - H are idempotent.

There are several other ways to express the vector of residuals e that will prove useful, including: e = y-y=y-Xß = y - Hy = (I −H)y Prove that the matrix H and I - H are idempotent.

Advanced Engineering Mathematics
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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There are several other ways to express the vector of residuals e that will prove useful, including: e = y-y = y-Xß = y - Hy = (I - H)y Prove that the matrix H and I - H are idempotent. Hint: In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if A * A = A
Transcribed Image Text:There are several other ways to express the vector of residuals e that will prove useful, including: e = y-y = y-Xß = y - Hy = (I - H)y Prove that the matrix H and I - H are idempotent. Hint: In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if A * A = A
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