Square Root of Matrices

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Offline msu_math

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Square Root of Matrices
« on: May 31, 2013, 11:27:58 AM »
Like numbers, definition of square root can be extended for matrices. A matrix B is said to be a square root of A if  B2=A. For example square roots of the matrix are , and their additive inverses.

There are a number of methods for calculating square roots of matrices. One of the frequently used method is diagonalization method. An n×n matrix A is diagonalizable if there is a matrix V and a diagonal matrix D such that A = VD-1V . This happens if and only if A has n eigenvectors which constitute a basis for Cn. In this case, V can be chosen to be the matrix with the n eigenvectors as columns, and a square root of A is VSV-1, where S is any square root of D. Indeed, (VD1/2V-1)2 = VD1/2(V-1V)D1/2V-1 = VDV-1 = A .

As in the example, the matrix can be diagonalized as , where and . D has principal square root , giving the square root .

Ref: Wikipedia
« Last Edit: May 31, 2013, 11:29:46 AM by msu_math »
Mohammad Salah Uddin

Lecturer in Mathematics
Department of Natural Sciences

Offline ashis3456

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Re: Square Root of Matrices
« Reply #1 on: November 17, 2013, 09:38:39 PM »
Thank you sir.it so much important for us........
Ashis Sarkar
Dept. of Textile Engineering
Daffodil International University
Student ID-131-23-3456
Diu email-ashis3456@diu.edu.bd

Offline proteeti

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Re: Square Root of Matrices
« Reply #2 on: March 28, 2014, 10:47:05 PM »

Offline Anuz

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Re: Square Root of Matrices
« Reply #3 on: November 29, 2015, 12:22:40 PM »
Nice to know...........
Anuz Kumar Chakrabarty
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Faculty of Science and Information Technology
Daffodil International University

Offline naser.te

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Re: Square Root of Matrices
« Reply #4 on: October 21, 2016, 12:50:20 PM »
Good post.
Abu Naser Md. Ahsanul Haque
Assistant Professor