Matrix each row magnitude 1

randomVector[len_] := RandomReal[{-10,10},{len}]

randomUnitVector[len_] := Module[
{vec = randomVector[len]},
vec/Norm[vec]
]

etest =randomUnitVector[6]

randomUnitMatrix[len_] := Table[randomUnitVector[len],{i,1,len}]

What was happening in code that does transformations in graphics

PolyhedronData["SnubCube"]

N@PolyhedronData["SnubCube"]//FullForm

snubCubePoints = Cases[N@PolyhedronData["SnubCube"],{a_/;NumberQ[a],b_/;NumberQ[b],c_/;NumberQ[c]},Infinity]

snubCubePolygons = Cases[N@PolyhedronData["SnubCube"],List[a__Integer],Infinity]

snubCubeColoredPolygons

snubCubeColoredPolygons = 
Table[{Glow[Hue[RandomReal[]]],Polygon[{snubCubePolygons[[i]]}]},{i,1,Length[snubCubePolygons]}];

snubGraphics[pts_] := Graphics3D[GraphicsComplex[pts,snubCubeColoredPolygons],Lighting-> None,ViewPoint-> Front]

snubGraphics[snubCubePoints]

rotmat =  RotationMatrix[Pi/3,{0,1,0}]

transformPoints[pts_, matrix_] := Table[matrix.pts[[i]],{i,1,Length[pts]}]

transformPoints[snubCubePoints,rotmat];

GraphicsRow[{snubGraphics[transformPoints[snubCubePoints,{{1,0,0},{0,1,0},{0,0,-1}}]],
snubGraphics[snubCubePoints]
}
]

refx = {{-1,0,0},{0,1,0},{0,0,1}};

refy = {{1,0,0},{0,-1,0},{0,0,1}};

refz = {{1,0,0},{0,1,0},{0,0,-1}};

GraphicsGrid[
{
{
snubGraphics[snubCubePoints],
snubGraphics[transformPoints[snubCubePoints,refx]]},
{
snubGraphics[transformPoints[snubCubePoints,refy]],
snubGraphics[transformPoints[snubCubePoints,refz]]
}
}
]

Dimensions[snubCubePoints]

newpoints= RandomReal[{-1,1},{56,3}];

Dimensions[newpoints]

snubGraphics[newpoints]

Eigenvalues

mymat ={{-1,-2},{6,9}}

Det[mymat]

Eigenvalues[mymat]

Eigenvectors[mymat]

{{-(3/2)+(1/6) (4+(Sqrt[13])),1},{-(3/2)+(1/6) (4-(Sqrt[13])),1}}//Simplify

mymat.Eigenvectors[mymat][[1]]

{-(1/2)+(1/6) (-4-(Sqrt[13])),9+6 (-(3/2)+(1/6) (4+(Sqrt[13])))}/(4+(Sqrt[13]))//Simplify

Eigensystem[mymat]

Plus@@(Sin[#/Pi]&)/@Range[10]