Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Consider the upper traingular $N \times N$ matrix

$$\left(\begin{array}{cccccccc} 0 & b_{1} & \dots & b_{q} & 0 & 0 & \dots & 0\\ \vdots & 0 & b_{1} & \dots & b_{q} & 0 & \dots & 0\\ \vdots & & \ddots & & & & & \vdots\\ \vdots & & & 0 & b_{1} & \dots & b_{q} & 0\\ \vdots & & & & 0 & b_{1} & \dots & b_{q}\\ \vdots & & & & & 0 & \dots & 0\\ \vdots & & & & & & \ddots & \vdots\\ 0 & \dots & \dots & \dots & \dots & \dots & \dots & 0 \end{array}\right)$$

Is there a name for matrices of this form?

share|improve this question
4  
"Weird upper triangular matrices..."? –  DonAntonio Oct 3 '13 at 17:08

3 Answers 3

The upper block has several properties that you can combine in a name:

strictly upper triangular, Toeplitz, band matrix with a right/upper bandwidth $q$.

However, if you want to describe the whole matrix, you lose the "Toeplitz" part. You might say

These matrices are of form

$$\begin{bmatrix} X \\ 0 \end{bmatrix}$$

where $0$ is a zero matrix of order $q \times n$, and $X$ is strictly upper triangular, Toeplitz, band matrix of order $(n-q) \times q$ with a right/upper bandwidth $q$.

However, I believe a formal, nameless description is far better.

share|improve this answer

There is, so far as I know, no standard name for this type of matrix. However, it is composed of the first $q$ superdiagonals of the matrix, so "q-superdiagonal matrix" might be a sensible thing to call them.

share|improve this answer

Strictly (zeros on the diagonal) upper triangular (obvious) banded (has a limited band) Toeplitz (is a diagonal-constant) matrix.

You can call it a StrUTriBaToM :-)

share|improve this answer
    
That's what I thought at first, but observe the zeroes in the bottom right block. That's why I had to amend my answer. –  Vedran Šego Oct 3 '13 at 17:23
    
Ah indeed, well then StrUTriBaToM could become StrUTriBATOM for strictly upper triangular banded almost Toeplitz matrix. –  Algebraic Pavel Oct 3 '13 at 17:27

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.