Fix: Unitary Decomposition -> Conj inplace not handled correct

src/Algebra/Matrices/NormalMatrices/FUnitaryMatrix.cs

@@ -110,10 +110,31 @@ public static partial class CategoryOf<TDimension>
             return new(U, logd);
         }
 
-        /*/// <inheritdoc />
-        public override JDPair<OnField<Complex>.FMatrix> EigenDecomposition() => this.UnitaryDecomposition();*/
+        /*
+         * /// <inheritdoc />
+         * public override JDPair<OnField<Complex>.FMatrix> EigenDecomposition() => this.UnitaryDecomposition();
+         * */
 
         internal override void UnitaryFix(OnField<Complex>.FMatrix a) => a.UnitaryFix();
+        protected override bool NeedPreNormalFix() => !Property.IsUnitary;
+        protected override void PreNormalConstructionFix()
+        {
+            if (Property.IsDiagonal)
+            {
+                for (int i = 1; i <= Dim; i++)
+                    this[i, i] /= (this[i, i] * Complex.Conjugate(this[i, i]));
+            }
+            else
+            {
+                this[1] = this[1].Normalize;
+                for (int i = 2; i <= Dim; i++)
+                {
+                    for (int j = 1; j < i; j++)
+                        this[i] -= this[i].ProjectionOn(this[j]);
+                    this[i] = this[i].Normalize;
+                }
+            }
+        }
     }
 }