ecoli Posted June 26, 2012 Share Posted June 26, 2012 Need help on a problem and I think there's some notation issues I'm having: [math] A=\sum _{i}^{r}\lambda _{i}\bold{u_{i}v_{i}}^{T} [/math] where A is a nxr matrix with (left and right) singular vectors v_1... v_r, u_1...u_r & lambda are singular values How does summation work in this case? Each product of rank-1 matrices results in a vector which, when summed, should result in a vector. But A is a matrix, so I feel like I must be missing something very simple about matrix addition. Link to comment Share on other sites More sharing options...
mississippichem Posted June 26, 2012 Share Posted June 26, 2012 (edited) The product "uv^T" gives an r x r matrix. You then have a sum of lamdas times that r x r matrix. Distribute the matrix over the sum of lamdas. I'll LaTeX the matrix out explicity if you neef further clarification. Edited June 26, 2012 by mississippichem 1 Link to comment Share on other sites More sharing options...
ecoli Posted June 26, 2012 Author Share Posted June 26, 2012 The product "uv^T" gives an r x r matrix. You then have a sum of lamdas times that r x r matrix. Distribute the matrix over the sum of lamdas. I'll LaTeX the matrix out explicity if you neef further clarification. Ah now its obvious. I was performing this calculation in R... apparently, a single column/row subset of a matrix in R is treated as a vector, not a single-entry matrix. So the transpose operation failed. Hence the confusion. Thanks! Link to comment Share on other sites More sharing options...
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