This article is cited in 3 papers

Generalized Jordan Matrix of a Linear Operator

S. G. Dalalyan

Yerevan State University

Abstract: For any linear operator defined over an arbitrary field $\mathbf k$, there is a basis in which this matrix is a generalized Jordan matrix (of the second kind) with elements in the field $\mathbf k$. For any linear operator, such a matrix is defined uniquely up to permutation of diagonal blocks.

Keywords: linear operator over a field, Jordan normal form, generalized Jordan matrix, Jordan cell, algebraically closed field, companion matrix, block-diagonal matrix, splitting field.

UDC: 512

Received: 06.10.2006

DOI: 10.4213/mzm3750

 English version: Mathematical Notes, 2007, 82:1, 25–32

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