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Do bidiagonal matrices like the one below have a name?

$$\left(\begin{array}{cccc} a_1 & a_2 & & & \\ & a_2 & a_3 & & \\ & & a_3 & a_4 & \\ & & & a_4 & a_5\\ & & & & a_5\\ \end{array}\right)$$

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I don't think so. Btw, one should be careful with the word "similar" when it comes to matrices, to avoid confusion. You probably wanted to ask "matrices like the one below". –  Vedran Ĺ ego Feb 6 at 2:33
    
Ah, yes, good point –  Jay Lemmon Feb 6 at 6:16

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