TL;DR
This paper introduces double circulant matrices, provides a formula for their rank, and explores their linear independence properties, also extending the concept to multiple circulant matrices and posing open questions.
Contribution
It presents the first detailed study of double circulant matrices, including rank computation and linear independence, and generalizes to multiple circulant matrices.
Findings
Rank formula for double circulant matrices
Any consecutive r rows are linearly independent
Extension to multiple circulant matrices
Abstract
Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a generalization, multiple circulant matrices are also introduced. Two questions on square double circulant matrices are suggested.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Graph theory and applications