A nearly singular Matrix:

|M	|	Cx|	Cy|	Cv|	Cu|	Ct|	Cz|
|R1	|	3.0|	5.3|	5.6|	3.5|	6.8|	5.7|
|R2	|	0.4|	8.2|	6.7|	1.9|	2.2|	5.3|
|R3	|	7.8|	8.3|	7.7|	3.3|	1.9|	4.8|
|R4	|	5.5|	8.8|	3.0|	1.0|	5.1|	6.4|
|R5	|	5.1|	5.1|	3.6|	5.8|	5.7|	4.9|
|R6	|	3.5|	2.7|	5.7|	8.2|	9.6|	2.9|

Splitting this up into Diagonal Form shows the EigenValues: 
{=MDiagonal(M:Cz) 
MU	CxU	CyU	CvU	CuU	CtU	CzU
R1U	|	-0.403927083187059|	-0.123898215609863|	0.287702622254744|	-0.200314519093036|	-0.537524234529712|	0.640047760341526|
R2U	|	-0.353729231942301|	0.373714276480282|	0.751239537361094|	0.209291680058067|	0.322161464947282|	-0.152516919360814|
R3U	|	-0.457605896131687|	0.38593372819565|	-0.47808462330915|	0.601434167131118|	-0.226632721090792|	-0.001283183600456|
R4U	|	-0.414094339280133|	0.321510801357695|	-0.200358974872614|	-0.714971304765253|	-0.0887913730022847|	-0.407363583813183|
R5U	|	-0.394852054935849|	-0.207078846634164|	-0.280702672275078|	-0.113860880510296|	0.732257990349585|	0.416233289425341|
R6U	|	-0.418250067127441|	-0.741479052334937|	0.0732375762447697|	0.173780787079552|	-0.10877327418446|	-0.477368376191145|

3.00000000000001	5.30000000000001	5.60000000000001	3.50000000000001	6.80000000000001	5.70000000000001	
0.400000000000005	8.20000000000001	6.70000000000001	1.90000000000001	2.20000000000001	5.30000000000001	
7.80000000000001	8.30000000000002	7.70000000000001	3.3	1.9	4.80000000000001	
5.50000000000001	8.80000000000001	3.00000000000001	1	5.1	6.40000000000001	
5.10000000000001	5.10000000000001	3.60000000000001	5.80000000000001	5.70000000000001	4.90000000000001	
3.5	2.70000000000001	5.70000000000001	8.20000000000001	9.60000000000002	2.90000000000001	

MU_D: {30.6345270060248;9.95413519810155;5.35026646242133;4.86732679833729;1.81968172373669;1.11959127302363}

MUV	CxUV	CyUV	CvUV	CuUV	CtUV	CzUV
R1UV	|	-0.348552419667681|	0.0909275122485802|	-0.905129284244408|	0.0552992879840771|	-0.212117645332546|	0.054152288504968|
R2UV	|	-0.510096761889621|	0.540704526724289|	0.134551163812195|	-0.155486053496374|	0.313932818646067|	-0.553720295051057|
R3UV	|	-0.430994698097156|	0.0777931276378289|	0.330644396438511|	0.687702629653246|	-0.46545440126706|	0.0963502782425255|
R4UV	|	-0.317609493220483|	-0.543460577627579|	-0.0693893116372843|	0.355621112134085|	0.686520114678987|	0.0344048042734964|
R5UV	|	-0.416918405953187|	-0.597330204713173|	0.14615884327692|	-0.490215128809234|	-0.38479291314885|	-0.244206476825847|
R6UV	|	-0.397315148288299|	0.202894698527313|	0.164723896828176|	-0.364765570162055|	0.14293018011675|	0.787627763921539|


}

The last Matrix is ortho-normal:

{=Transpose(MUV:CzUV) 
MUV⁺	|R1UV	|R2UV	|R3UV	|R4UV	|R5UV	|R6UV	|
CxUV	|	-0.348552419667681|	-0.510096761889621|	-0.430994698097156|	-0.317609493220483|	-0.416918405953187|	-0.397315148288299|
CyUV	|	0.0909275122485802|	0.540704526724289|	0.0777931276378289|	-0.543460577627579|	-0.597330204713173|	0.202894698527313|
CvUV	|	-0.905129284244408|	0.134551163812195|	0.330644396438511|	-0.0693893116372843|	0.14615884327692|	0.164723896828176|
CuUV	|	0.0552992879840771|	-0.155486053496374|	0.687702629653246|	0.355621112134085|	-0.490215128809234|	-0.364765570162055|
CtUV	|	-0.212117645332546|	0.313932818646067|	-0.46545440126706|	0.686520114678987|	-0.38479291314885|	0.14293018011675|
CzUV	|	0.054152288504968|	-0.553720295051057|	0.0963502782425255|	0.0344048042734964|	-0.244206476825847|	0.787627763921539|
}

{=MMult(MUV:CzUV,MUV⁺:R3UV) 
MUV_MUV⁺	MUV_R1UV	MUV_R2UV	MUV_R3UV
R1UV_MUV⁺	|	1|	3.33066907387547E-16|	-3.60822483003176E-16|
R2UV_MUV⁺	|	3.33066907387547E-16|	1|	1.02695629777827E-15|
R3UV_MUV⁺	|	-3.60822483003176E-16|	1.02695629777827E-15|	1|
R4UV	|	1.2490009027033E-16|	3.33066907387547E-16|	5.55111512312578E-16|
R5UV	|	-6.93889390390723E-16|	-5.55111512312578E-17|	7.7715611723761E-16|
R6UV	|	4.44089209850063E-16|	1.38777878078145E-16|	8.60422844084496E-16|
}

Measurement Matrix scaled by the EigenValues: 

{=MultDiag(MU:CzU,MU_D) 
MU_	CxU_	CyU_	CvU_	CuU_	CtU_	CzU_
R1U_	|	-12.3741151383588|	-1.23329958898411|	1.53928569100023|	-0.974996226877581|	-0.978123025639271|	0.716591886796692|
R2U_	|	-10.8363277087568|	3.72000243354543|	4.01933170198798|	1.01869100301566|	0.586231329856807|	-0.170756611904816|
R3U_	|	-14.0185401831623|	3.84163650796688|	-2.55788012629028|	2.92737663911296|	-0.412399420569629|	-0.00143664116075758|
R4U_	|	-12.6855842197192|	3.20036198436447|	-1.07197390370606|	-3.47999899172609|	-0.161572038677745|	-0.45608071338487|
R5U_	|	-12.0961059403167|	-2.0612908360634|	-1.5018340933854|	-0.554198114990044|	1.3324764820993|	0.466011158382531|
R6U_	|	-12.8128929766873|	-7.38078273350218|	0.391840547971416|	0.84584788198845|	-0.197932739064462|	-0.534457468001067|
}

The Product of all 3 Matrices yields the original Matrix: 

{=MMult(MU_:CzU_,MUV⁺:R3UV) 
MU__MUV⁺	MU__R1UV	MU__R2UV	MU__R3UV
R1U__MUV⁺	|	3.00000000000001|	5.30000000000003|	5.60000000000003|
R2U__MUV⁺	|	0.39999999999999|	8.2|	6.70000000000001|
R3U__MUV⁺	|	7.79999999999999|	8.3|	7.69999999999999|
R4U_	|	5.49999999999999|	8.8|	3.00000000000001|
R5U_	|	5.10000000000003|	5.10000000000005|	3.60000000000004|
R6U_	|	3.50000000000001|	2.70000000000002|	5.70000000000002|
}

{=MU__R1UV=Cx {TRUE;TRUE;TRUE;TRUE;TRUE;TRUE}}
{=MU__R1UV:MU__R3UV=Cx:Cz {TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE;TRUE,TRUE,TRUE}}
This is a Sample *.STX File. (C) http://Spoc-Web.com