# Decomposing an upper triangular Toeplitz matrix into a product of matrices

Skirting the boundaries of being too broad a question, is there any nice way of decomposing a matrix structured as shown below into a product of two or more matrices?

$$M = \begin{bmatrix} v_1 & v_2 & v_3 & \dots & v_n \\ 0 & v_1 & v_2 & \dots & v_{n-1} \\ 0 & 0 & v_1 & \dots & v_{n-2} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \dots &v_1 \\ \end{bmatrix}$$

Is there a special name for such matrices? Where can I read more about them?

• Why even decompose it? What is the motivation? – Rodrigo de Azevedo Aug 15 '17 at 10:37
• @RodrigodeAzevedo I was working on a problem that involved diagonalizing circulant matrices (which I recently learnt about) and I was trying to extend the result to other transforms similar to the Fourier transform, which is where I encountered the above matrix. Maybe I should have mentioned the motivation in the question, I was afraid it would not really help with clarifying things. – Television Aug 15 '17 at 11:17