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Undergraduate
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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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adjacency matrix
matrices
matrix multiplication
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Undergraduate
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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 …
Mathematics
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