Gram-Schmidt Process in Two Dimensions

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

The Gram-Schmidt process is a means for converting a set of linearly independent vectors into a set of orthonormal vectors. If the set of vectors spans the ambient vector space, then this produces an orthonormal basis for the vector space. The Gram-Schmidt process is a recursive procedure. After the first vectors have been converted into orthonormal vectors, the difference between the original vector and its projection onto the space spanned by the first orthonormal vectors is normalized to obtain the vector in the orthonormal collection. In two dimensions, start with a vector and normalize it to obtain . Next, project onto and compute , the difference between and this projection. Finally, normalize this vector to obtain .

Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send