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Is every matrix similar to a Toeplitz matrix?

โœ Scribed by D.Steven Mackey; Niloufer Mackey; Srdjan Petrovic

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
151 KB
Volume
297
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

We show that every n ร‚ n complex nonderogatory matrix is similar to a unique unit upper Hessenberg Toeplitz matrix. The proof is constructive, and can be adapted to nonderogatory matrices with entries in any ยฎeld of characteristic zero or characteristic greater than n. We also prove that every n ร‚ n complex matrix with n T 4 is similar to a Toeplitz matrix.

๐Ÿ“œ SIMILAR VOLUMES

Every unit matrix is a LULU
Every unit matrix is a LULU
โœ Gilbert Strang ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 288 KB

The four matrices LoUoL1U1 at the end of the title are triangular with ones on their main diagonals. Their product has determinant one. Following a question and theorem of Toffoli, we show that any matrix with determinant one can be factored in this way. A transformation of the plane becomes a seque

Almost every unit matrix is a ULU
Almost every unit matrix is a ULU
โœ Tommaso Toffoli ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 443 KB

We call an n X n matrix a shear if it is triangular with all l's on the diagonal, and a unit matrix if it has unit determinant. Earlier we had shown that, for n = 3, every orthogonal matrix (except for degenerate cases when one of the Euler angles equals rr) can be written in the form U,,LU,, where

Every matrix is a linear combination of
Every matrix is a linear combination of three idempotents
โœ Vyacheslav Rabanovich ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 173 KB

It is shown that every n ร— n matrix over a field of characteristic zero is a linear combination of three idempotent matrices. It is proved that both 2 ร— 2 matrices and complex 3 ร— 3 matrices are linear combinations of two idempotents. Also we present 3 ร— 3 and 4 ร— 4 matrices that are not linear comb