R help - Feb 2011 - How column names/row names are preserved in matrix calculation?

Can somebody tell me that, if I do some arithmetic calculation over 2
matrices then how the column names and row names are preserved? It seems
that, for multiplication, column names and row names of the 2nd matrix are
preserved and for additional, there seems not having any explicit rule:

 
> set.seed(1)
> dat1 <- matrix(rnorm(25), 5); colnames(dat1) = rownames(dat1)
paste("mat1", 1:5, sep="")
> dat2 <- matrix(rnorm(25), 5); colnames(dat2) = rownames(dat2)
paste("mat2", 1:5, sep="")
> dat3 <- matrix(rnorm(25), 5); colnames(dat3) = rownames(dat3)
paste("mat3", 1:5, sep="")
> dat1
           mat11      mat12      mat13       mat14       mat15

mat11 -0.6264538 -0.8204684  1.5117812 -0.04493361  0.91897737

mat12  0.1836433  0.4874291  0.3898432 -0.01619026  0.78213630

mat13 -0.8356286  0.7383247 -0.6212406  0.94383621  0.07456498

mat14  1.5952808  0.5757814 -2.2146999  0.82122120 -1.98935170

mat15  0.3295078 -0.3053884  1.1249309  0.59390132  0.61982575
> dat2
            mat21       mat22      mat23      mat24      mat25

mat21 -0.05612874  1.35867955 -0.4149946 -0.1645236 -0.7074952

mat22 -0.15579551 -0.10278773 -0.3942900 -0.2533617  0.3645820

mat23 -1.47075238  0.38767161 -0.0593134  0.6969634  0.7685329

mat24 -0.47815006 -0.05380504  1.1000254  0.5566632 -0.1123462

mat25  0.41794156 -1.37705956  0.7631757 -0.6887557  0.8811077
> dat1 %*% dat2 + dat3
           mat21      mat22      mat23       mat24      mat25

mat11 -1.2567987  0.5365897  3.5473394  0.89542630  2.5962144

mat12 -0.9370075 -1.0928568  0.2483355 -2.23467503  0.3284073

mat13  0.7665543 -2.6496778  1.8774045  1.45703219  0.9533289

mat14  0.7245671  4.5147054 -1.3445549  0.02866729 -5.3999956

mat15 -0.2173109 -0.1053570  0.3000135  2.88350373 -0.2541405

 

Can somebody finalize me what is the **rule** for preserving column names
and row names for matrix arithmatics?

 

Thanks,


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