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Gram-Schmidt Calculator

Generate orthogonal and orthonormal vectors.

Run Gram-Schmidt

One vector per line, values separated by spaces

One vector per line, values separated by spaces

How to Use

  1. Enter vectors as rows separated by new lines
  2. Submit to get orthogonal and normalized results
  3. Copy the basis for further calculations

Process overview

Gram-Schmidt subtracts projections to build perpendicular vectors.

Normalization

Each orthogonal vector is scaled to unit length to form an orthonormal set.

Frequently Asked Questions

Do vectors need to be independent?
Dependent vectors will create zeros; the calculator still returns a basis for the span.
Which dimensions are supported?
Any consistent dimension works as long as all vectors share the same length.

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