23. Consider the problem of finding the vector x of minimum norm satisfying (x|y) 2 6. -1, 2,...," where the y's are linearly independent. (a) Show that this problem has a unique solution. (b) Show that a necessary and sufficient condition that be the solution is that the vector a with components a, satisfy G'a 2e a20 and that a, - 0 if (x)y) > e. Gis the Gram matrix of (y, Y2,..., y).

23. Consider the problem of finding the vector x of minimum norm satisfying (x|y) 2 6. -1, 2,...," where the y's are linearly independent. (a) Show that this problem has a unique solution. (b) Show that a necessary and sufficient condition that be the solution is that the vector a with components a, satisfy G'a 2e a20 and that a, - 0 if (x)y) > e. Gis the Gram matrix of (y, Y2,..., y).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 24EQ

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