Our null space calculator tool will help you find the null space of a given matrix efficiently.

## How to Use the Null Space Calculator

Enter the matrix for which you wish to find the null space. Input each row of the matrix separated by commas, and each element within the rows separated by spaces. For example, for a 2×3 matrix:

1 2 3,4 5 6

After entering the matrix, click the “Calculate” button. The result will appear in the “Result” field below the button. Each row in the “Result” field represents a vector in the basis of the null space.

## How the Calculator Works

The calculator employs the Gaussian elimination method to reduce the input matrix to row echelon form. Once the matrix is in this form, the calculator identifies free variables (variables that can take on any value) and pivot variables, and uses these to form a basis for the null space.

## Limitations

The calculator does not perform symbolic computations and is limited by numerical precision and rounding errors inherent in JavaScript’s floating-point arithmetic. It is best suited for integer matrices or matrices with precise floating-point numbers. The number of rows and columns should be reasonably small to prevent performance issues. Results might be inaccurate for ill-conditioned matrices where small changes in the input can lead to large changes in results.