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**Basic Maths / Square Root of Matrices**

« **on:**May 31, 2013, 11:27:58 AM »

Like numbers, definition of

There are a number of methods for calculating square roots of matrices. One of the frequently used method is diagonalization method. An

As in the example, the matrix can be diagonalized as , where and .

Ref: Wikipedia

**square root**can be extended for matrices. A matrix**B**is said to be a square root of**A**if**B**. For example square roots of the matrix are , and their additive inverses.^{2}=AThere 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**. This happens if and only if^{-1}V**A**has**n**eigenvectors which constitute a basis for**C**. In this case,^{n}**V**can be chosen to be the matrix with the**n**eigenvectors as columns, and a square root of**A**is**VSV**, where^{-1}**S**is any square root of**D**. Indeed,**(VD**.^{1/2}V^{-1})^{2}= VD^{1/2}(V^{-1}V)D^{1/2}V^{-1}= VDV^{-1}= AAs in the example, the matrix can be diagonalized as , where and .

**D**has principal square root , giving the square root .Ref: Wikipedia