# zerobasis: Orthonormal Matrix with Columns Summing to Zero In fda: Functional Data Analysis

 zerobasis R Documentation

## Orthonormal Matrix with Columns Summing to Zero

### Description

The matrix is k by k-1, columns are orthonormal and sum to zero. This matrix is used when quantities are unchanged to adding a constant, such as in multinomial data modelling.

### Usage

``````zerobasis(k)
``````

### Arguments

 `k` A positive integer greater than one.

### Details

There are many ways of generating these matrix. This functions uses the discrete Fourier series less the constant vector.

### Value

A `k` by `k-1` matrix with orthonormal columns that sum to zero.

### References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

`smooth.surp`, `eval.surp`