INTERNATIONAL IEC STANDARD 61089.pdfl

INTERNATIONAL IEC STANDARD 61089.pdfl


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INTERNATIONAL IEC STANDARD 61089.pdfl

INTERNATIONAL IEC STANDARD 61089.pdf. 9  dec . 2010  02 15  22  11  07  46  01  22. STANDARD — International Electrotechnical Commission (IEC). 2010  01 11.
This is a free PDF file of international standard “IEC 61089 ”. It can be viewed and printed on your PC.download international standard for pdfQ:

How do I calculate the value of homology of a matrix over $\mathbb{Q}$?

Let $A$ be a matrix over $\mathbb{Q}$ which represents the boundary map between homology groups of the chain complex of a simplicial complex $\Delta$. What is the formula to calculate the value of the action of the boundaries on $\alpha$?
As an example if I take a 7-simplex with vertices $0,1,2,3,4,5,6$, I’d expect that it gives me
$$
\begin{pmatrix}
1 & 0 & 1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 1
\end{pmatrix},
$$
so $\partial^7(\alpha) = \left(\begin{array}{c}-\alpha(1) \\ -\alpha(0) \\ -\alpha(2) \\ -\alpha(3) \\ -\alpha(4) \\ -\alpha(5) \\ -\alpha(6) \end{array}\right)$. Now I know that the differential should be an alternating matrix as it is for homology groups, but I don’t know which formula to use.

A:

Some further details on your example. You can think of $\alpha$ as a linear map $C_3 \to C_1$. Its action on an element $c \in C_3$ is $c\mapsto \partial c$ and its adjoint action is $\alpha^*(\partial) = \partial \

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