# H

## Hadamard Matrix

An *n*x*n* matrix with entries either 1 or -1
where each row is orthogonal to every other row. Of course,
a row's inner product with *itself* is *n*.
So when you multiply a Hadamard matrix times it's transpose
you get *n* times the identity matrix.

## Hamiltonian Chain

A chain in a graph such that the nodes
of the chain comprise all the nodes of the graph.

## Hamiltonian Cycle

A cycle in a graph such that the nodes
of the cycle comprise all the nodes of the graph.

## Hamming Distance

In a binary code a distance can be defined
between code words, given two words *v* and *w* the
Hamming distance, *d(v,w)* is the number of positions in which
they differ.

For instance:

0100110110111 and
0010110110111

are at Hamming distance 2 from one another.

## Homeomorph

A graph obtained from another by inserting new nodes along existing edges.
The following graph is a homeomorph of * K(5) *.

## Hypercube

A regular polytope,
the convex hull of the points
*(e*_{1},...,e_{d}) where each coordinate
*e*_{i} is either 0 or 1.

## Hyperplane

A *(d-1)*-dimensional flat in *R*^{d}.

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An On-line Dictionary of Combinatorics