# xpnd¶

## Purpose¶

Expands a column vector into a symmetric matrix.

## Format¶

x = xpnd(v)
Parameters: v (Kx1 vector) – data to be expanded into a symmetric matrix. x (MxM matrix) – the results of taking v and filling in a symmetric matrix with its elements. $M = \frac{\sqrt{1 + 8 \times K} - 1}{2}$

## Examples¶

x = { 1,
2, 3,
4, 5, 6,
7, 8, 9, 10 };
y = xpnd(x);


After the code above, the variables x and y are equal to:

    1
2
3
4       1   2   4   7
x = 5   y = 2   3   5   8
6       4   5   6   9
7       7   8   9  10
8
9
10


## Remarks¶

If v does not contain the right number of elements, (that is, if $$\sqrt{1 + 8 \times K}$$ is not integral), then an error message is generated.

This function is particularly useful for hard-coding symmetric matrices, because only about half of the matrix needs to be entered.

Functions vech()