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.…

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. =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 42EQ

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Question

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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