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Undergraduate
By Shiva Kintali on Oct. 1, 2013 | Updated Jan. 4, 2018

Graphs, Matrices and Walks

Let \(G\) be a directed graph (possibly with self-loops) with vertices \(v_1, \dots , v_n\). Let \(M\) be the adjacency matrix of \(G\). Prove that \(M_{ij}^k\) (i.e., that \([i][j]^{th}\) entry of …
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Undergraduate
By True Putnam on June 24, 2013 | Updated Jan. 4, 2018

Putnam 2005 A4

Let \(H\) be an \(n \times n\) matrix all of whose entries are \(\pm 1\) and whose rows are mutually orthogonal. Suppose \(H\) has an \(a \times b\) sub matrix whose entries are all \(1\). Show that …
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