User:Sintel/CTE tuning: Difference between revisions

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 <math>
 \begin{align}
-& \text{minimize}   && \left\|   g\mathrm{V} - \mathrm{J}   \right\|   \\[8pt]
+& \underset{g}{\text{minimize}}   && \left\|   g\mathrm{V} - j   \right\|^2   \\
-& \text{subject to} &&  (g\mathrm{A} - \mathrm{J}_0)b_i = 0, \quad i = 1, \dots, r
+& \text{subject to} &&  (g\mathrm{A} - j_0)b_i = j_0, \quad i = 1, \dots, m \\
 \end{align}
 </math>
-where G is the generator list, V = AW the Tenney-weighted temperament mapping, J = J<sub>0</sub>W the Tenney-weighted [[JIP]], and B the monzo list.
+where ''g'' is the generator list, V = AW the Tenney-weighted temperament mapping, ''j'' = ''j''<sub>0</sub>W the Tenney-weighted [[JIP]], and <math>b_i</math> is the ''i''-th monzo. If we stack all the ''b''s into a matrix B, then the problem can be solved using he method of lagrange multipliers.
 The problem is feasible if
 # rank (B) ≤ rank (A), and
-# Each column in B and N (A) are [[Wikipedia:linear independence|linearly independent]].
+# A has full rank.
 == Computation ==