Educational > Basic Maths

Square Root of Matrices

(1/1)

msu_math:
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

ashis3456:
Thank you sir.it so much important for us........

proteeti:
bah!

Anuz:
Nice to know...........

naser.te:
Good post.

Navigation

[0] Message Index