ers and rearrange or redistribute the number string in rows and columns SO that they are more easily processed. In other words, a Hadamard transform is a transform that exploits the properties of a Hadamard matrix in the same way that a Fourier transform exploits the properties of the Fourier number series (the ability to describe waveforms as a summation of sines and cosines). 3.2.3 The Properties of a Hadamard Matrix Hadamard matrices possess a number of useful properties. Hadamard matrices are symmetric, which means that specific rows can be matched to specific columns. Hadamard matrices are orthogonal, which means that the binary product between any two rows equals zero. The binary product is simply the result of multiplying all the components of two vectors, in this case rows, together and adding the results. We will see why this is useful later. Interrelationship of the Physical Layer with Other Layers of the OSI Model This means that if you compare any two rows, they match in exactly N/2 places and differ in exactly N/2 places SO the 'distance' between them is exactly N/2. We explain why 'distance' is useful later. Exactly half of the places that match are +1s and the other half are - 1s. Exactly half of the places that differ are (-1+1) pairs and exactly half are (+1-1) pairs (the symmetric properties of the matrix). You can turn a Hadamard matrix upside down (reverse the +1s and 1s) and it will still work. The matrix has the property of sequency. The sequence number of each row is the product of the number of transitions from +1 to in that row. A row's sequence number is called its sequency because it measures the number of zero crossings in a given interval. Each row has its own unique sequency value that is separate from its natural order (the row number). The Hadamard transform can therefore be correctly described as a sequency transform that is directly analogous to describing the Fourier transform as a frequency transform. In other words, given that the rows in a Hadamard matrix are orthogonal, the 