In reply to Cesana Bruno mario.

Thank you! I have updated the post to display the correct matrix.

The matrix you saw was the square-root matrix for the 6x6 Toeplitz matrix generated by {6,5,4,3,2,1}. I later updated the program to use the 7x7 Toeplitz matrix generated by {4,3,2,1,0,-1,2}. However, I forgot to update the image. The square-root matrix for the first matrix has all positive entries. The square-root matrix for the second matrix has some negative entries, which is why I decided to switch examples.