Use this Gram-Schmidt calculator to transform your set of vectors into an orthogonal set through a straightforward process.

## Gram-Schmidt Process Calculator

**How to use the Gram-Schmidt Process Calculator:**

- Enter the components of your vectors, separated by commas. For example, for a 3-dimensional vector (1,2,3), simply input “1,2,3”.
- Optional: Add a third vector if you are working in a three-dimensional space.
- Click the ‘Calculate’ button to perform the Gram-Schmidt process on your vectors.
- Results will be displayed in the ‘Result’ area, where each orthogonal vector is presented on a new line.

**How the Calculator Works:**

The calculator takes the input vectors and applies the Gram-Schmidt process to them, which is a method for orthonormalizing a set of vectors in an inner product space. The process projects each vector onto the space orthogonal to the space spanned by the previous vectors in the set. It effectively turn a set of linearly independent vectors into a set of orthogonal vectors.

**Limitations:**

The calculator is designed for educational and illustrative purposes. It is limited by the precision of JavaScript number representation (floating-point arithmetic) and might not handle very large numbers or vectors with very small magnitudes accurately. Additionally, the input is currently limited to three vectors in order to keep the user interface simple.