# OrthogonalProjections (3) - Linux Man Pages

## NAME

QuantLib::OrthogonalProjections -

## SYNOPSIS

#include <ql/math/matrixutilities/basisincompleteordered.hpp>

### Public Member Functions

**OrthogonalProjections** (const **Matrix** &originalVectors, **Real** multiplierCutOff, **Real** tolerance)

const std::vector< bool > & **validVectors** () const

const std::vector< **Real** > & **GetVector** (Size index) const

Size **numberValidVectors** () const

## Detailed Description

Given a collection of vectors, w_i, find a collection of vectors x_i such that x_i is orthogonal to w_j for i != j, and <x_i, w_i> = <w_i, w_i>

This is done by performing GramSchmidt on the other vectors and then projecting onto the orthogonal space.

This class is tested in

MatricesTest::testOrthogonalProjection();

## Author

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