Abstract
Let us now consider a more interesting example of a graph G, one whose eigenvalues have come up in a variety of applications. Let \(\mathbb{Z}_{2}\) denote the cyclic group of order 2, with elements 0 and 1 and group operation being addition modulo 2.
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Notes
- 1.
For abelian groups other than \({\mathbb{Z}_{2}}^{n}\) it is necessary to use complex numbers rather than real numbers. We could use complex numbers here, but there is no need to do so.
- 2.
Recall from linear algebra that nonzero orthogonal vectors in a real vector space are linearly independent.
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Stanley, R.P. (2013). Cubes and the Radon Transform. In: Algebraic Combinatorics. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6998-8_2
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