# Manuals/calci/SHIFT

MATRIX("SHIFT",order)

• is the size of the Shift matrix.

## Description

• This function returns shift matrix of order 3.
• A shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere.
• A shift matrix U with ones on the superdiagonal is an upper shift matrix.
• The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix.
• Let Z is a shift matrix , then are equal to the matrix A shifted one position down, up left, right, and down along the main diagonal respectively.
• The alternative subdiagonal matrix L is unsurprisingly known as a lower shift matrix.
• The component of U and L are: .


where is the Kronecker delta symbol.

• For example, the 5×5 shift matrices are  • All shift matrices are nilpotent; an n by n shift matrix S becomes the null matrix when raised to the power of its dimension n.

## Examples

• 1.MATRIX("shift") = 0
• 2.MATRIX("shift",3)
 0 1 0 0 0 1 0 0 0
• 3.MATRIX("shift",7)
 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0