# Talk:Mason's gain formula

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## Mason

Q: who is "Mason"?

The Wikipedia on Mason's Invariant has a detailed biography on Samuel Jefferson Mason.

Δk= cofactor of the kth forward path determinant of the graph with the loops touching the kth forward path removed, that is, the factor Δk is obtained from Δ by removing the loops that touch path Pk.

## Woah copywrite problems!

Several sections (most) of this article seem to be pulled directly from a text, complete with references to non-existant figures.

It needs better citation and much better digestion. Figures would be especially helpful for this topic. If the original author could scan them, it would be of help.

98.84.125.52 (talk) 07:44, 16 February 2011 (UTC)

That section seems to be broken. I am removing most of it. Specifically:
• remove references to non-existant figure 2 and language that is meaningless without figure 2.
• remove language that explains how to create a signal flow graph. That should be covered in the article on signal flow graphs.
• reduced language about using signal flow graphs to analyze discrete data filters. That should go in an article on signal flow graphs or discrete data processing.
• convert I, we and us to third person
• remove language that is redundent with the opening paragraph
• remove verbal description of using Mason's Gain Formula that is covered in the preceeding section. Constant314 (talk) 19:06, 7 March 2011 (UTC)

## origin of matrix equation

that matrix equation form of mason's rule is very powerful, can someone cite an explanation or source of that claim? also the term transient matrix as well as transmittance is not defined or linked to a definition. —Preceding unsigned comment added by 76.120.250.40 (talk) 12:45, 3 February 2010 (UTC)

I found a simple proof of the matrix form of the theorem, but I haven't been able to independently verify it. The signal-flow graph consists of internal states ${\textstyle x}$ and input states ${\textstyle s}$. The input states may be connected to internal states with edges of unit weight and no edge may terminate in the input states. Now if transient matrix ${\textstyle T}$is determined by writing the system of equations for the states in matrix form,
${\displaystyle Tx+s=x}$
then the gain is determined by expressing ${\textstyle x}$ as a multiple of ${\textstyle s}$. Solving the matrix equation for ${\textstyle x}$,
${\displaystyle \left(I-T\right)x=s,}$
the gain matrix, ${\textstyle U}$, is then given by
${\displaystyle U=\left(I-T\right)^{-1}.}$

Gkaf (talk) 20:40, 14 March 2017 (UTC)

Simple math that can be verified by other editors such as conversion of feet to meters is allowed. But a proof of this equation is likely to be too complicated to be allowed without a citation to a reliable secondary source. However, the section needs improvement, especially definitions. For example, what is the meaning of the gain from node m to node n when node m is not an input? Constant314 (talk) 22:38, 14 March 2017 (UTC)