Could you explain how to show this in detail? It is from the book "Linear algebra done right" by Axler Suppose P = L(V) is such that P² = P. Prove that there is a subspaceU of V such that PPu if and only if P is self-adjoint.=

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Answered: Suppose P = L(V) is such that P² = P.…

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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Could you explain how to show this in detail? It is from the book "Linear algebra done right" by Axler

Suppose P = L(V) is such that P² = P. Prove that there is a subspace
U of V such that P
Pu if and only if P is self-adjoint.
=

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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