**HP Prime: Matrices Built from Shifted Elements**

**Introduction**

The programs LSM (left-shift matrix) and RSM (right-shift matrx) create a n x n matrix based on the elements of a given list. Each row has each of the elements rotated one element.

For LSM, each row has the elements shifted to the left one element.

For RSM, each row has the elements shifted to the right one element.

The illustration below shows how to programs work.

**HP Prime Program: LSM**

EXPORT LSM(L0)

BEGIN

// EWS 2019-03-02

// left shift matrix

LOCAL L1,N,M0,K;

N:=SIZE(L0);

L1:=L0;

FOR K FROM 1 TO N-1 DO

L1:=CONCAT(tail(L1),head(L1));

L0:=CONCAT(L0,L1);

END;

M0:=list2mat(L0,N);

RETURN M0;

END;

**HP Prime Program: RSM**

EXPORT RSM(L0)

BEGIN

// EWS 2019-03-03

// right shift matrix

LOCAL L1,N,M0,K;

N:=SIZE(L0);

L1:=L0;

FOR K FROM 1 TO N-1 DO

L1:=REVERSE(CONCAT(

tail(REVERSE(L1)),

head(REVERSE(L1))

));

L0:=CONCAT(L0,L1);

END;

M0:=list2mat(L0,N);

RETURN M0;

END;

Note: The program RSM creates a circulant matrix.

**Example**

list = {1, 7, 8, -2, 0}

LSM({1, 7, 8, -2, 0} returns:

[ [ 1, 7, 8, -2, 0 ]

[ 7, 8, -2, 0, 1 ]

[ 8, -2, 0, 1, 7 ]

[ -2, 0, 1, 7, 8 ]

[ 0, 1, 7, 8, -2 ] ]

RSM({1,7,8,-2,0}) returns:

[ [ 1, 7, 8, -2, 0 ]

[ 0, 1, 7, 8, -2 ]

[ -2, 0, 1, 7, 8 ]

[ 8, -2, 0, 1, 7 ]

[ 7, 8, -2, 0, 1 ] ]

Eddie

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