Hi,

Here's verified code : Let z = s$d * t(s$v). We showed a derivation demonstrating that because is orthogonal, the distance between e[,3] and e[,45] is the same as the distance between y[,3] and y[,45], which is the same as z[,3] and z[,45]:

library(tissuesGeneExpression)
data(tissuesGeneExpression)
y = e - rowMeans(e)
s = svd(e)
z = s$d * t(s$v)
a=sqrt(crossprod(e[,3]-e[,45]))
b=sqrt(crossprod(y[,3]-y[,45]))
c=sqrt(crossprod(z[,3]-z[,45]))

Is that transposable to row distances ? for example :

y1 =e - colMeans(e)
z1 = (s*u)  * (s$d)
a1=sqrt(crossprod(e[3,]-e[45,]))
b1=sqrt(crossprod(y1[3,]-y1[45,]))
c1=sqrt(crossprod(z1[3,]-z1[45,]))

a1 and b1 equals but not c1. What calculation should be done on z1 to be equals with a1 and b1 ?

Thanks a lot Lenny

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