(a) An n x n matrix B is a square root of a matrix A if B² = A. Show that the 2 x 2 identity matrix I2 has an infinite number of real square roots. (b) Adapt your proof from Part (a) to show that if n > 3 then the n x n identity matrix In also has an infinite number of real square roots.
(a) An n x n matrix B is a square root of a matrix A if B² = A. Show that the 2 x 2 identity matrix I2 has an infinite number of real square roots. (b) Adapt your proof from Part (a) to show that if n > 3 then the n x n identity matrix In also has an infinite number of real square roots.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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