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# dsqrtm

## PURPOSE Fréchet derivative of the matrix square root.

## SYNOPSIS function D = dsqrtm(X, H)

## DESCRIPTION ``` Fréchet derivative of the matrix square root.

function D = dsqrtm(X, H)

Computes the directional derivative (the Fréchet derivative) of sqrtm at
X along H (square matrices).

Thus, D = lim_(t -> 0) (sqrtm(X + tH) - sqrtm(X)) / t.

See also: dfunm dlogm dexpm```

## CROSS-REFERENCE INFORMATION This function calls:
• dfunm Fréchet derivative of matrix functions.
This function is called by:

## SOURCE CODE ```0001 function D = dsqrtm(X, H)
0002 % Fréchet derivative of the matrix square root.
0003 %
0004 % function D = dsqrtm(X, H)
0005 %
0006 % Computes the directional derivative (the Fréchet derivative) of sqrtm at
0007 % X along H (square matrices).
0008 %
0009 % Thus, D = lim_(t -> 0) (sqrtm(X + tH) - sqrtm(X)) / t.
0010 %
0011 % See also: dfunm dlogm dexpm
0012
0013 % This file is part of Manopt: www.manopt.org.
0014 % Original author: Nicolas Boumal, July 3, 2015.
0015 % Contributors:
0016 % Change log:
0017
0018     D = dfunm(@sqrtm, X, H);
0019
0020 end```

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