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Minimize tr{R} subject to_{yx}RR=^{T}RI

This problem is known as Procruses Analysis and can be solved using Lagrange Multipliers, so there's a tendency to write the following function:

L(R) = tr{R} - [itex]\Lambda[/itex](_{yx}RR-^{T}RI),

where [itex]\Lambda[/itex] is a matrix of Lagrange Multipliers

However, there is obviously a flaw in this, because the first parcel is a scalar, whilst the second is a square matrix.

So the question is: What is the correct form of the Lagrange equation? I'm familiar with this subject, but this example baffles me. I've searched in some mathematics books, but they only explain for scalar field subject to simpler equations.

If there's any problem with this post, let me know, please.

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# Procrustes Analysis and Lagrange Multipliers

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