Given U_1, ..., U_m, a collection of subspaces of some vector space V, recall that U_1 + ... + U_m is defined to be the space of all vectors which can be expressed as u_1 + ... + u_m where each u_k is a vector in the subspace U_k. Well U_1 + ... + U_m is called a direct sum if each of its vectors can be expressed uniquely as u_1 + ... + u_m. Give a specific example of a direct sum of vector subsp

Given U_1, ..., U_m, a collection of subspaces of some vector space V, recall that U_1 + ... + U_m is defined to be the space of all vectors which can be expressed as u_1 + ... + u_m where each u_k is a vector in the subspace U_k. Well U_1 + ... + U_m is called a direct sum if each of its vectors can be expressed uniquely as u_1 + ... + u_m. Give a specific example of a direct sum of vector subsp

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 4EQ: In Exercises 1-4, let S be the collection of vectors in [xy]in2 that satisfy the given property. In...

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