Null Space Calculator
Compute the null space (kernel) of a matrix. Enter a matrix and get its null space basis vectors.
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How to use this tool?
- 1 Enter the requested data in the fields above carefully.
- 2 Click the calculate button to process the information instantly.
- 3 Analyze the detailed result and the formula explanation presented below.
- 4 You can print, share, or even embed the calculator on your own site for free.
Unlike traditional static calculators, our tools adapt to specific user needs. They include detailed explanations of the formulas used, ensuring transparency in results. Furthermore, our design is focused on user experience, eliminating distractions and focusing on what really matters: your data and conclusions.
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Frequently Asked Questions
The null space (or kernel) of a matrix A is the set of all vectors x such that Ax = 0. It includes the zero vector and all linear combinations of the basis vectors.
The null space is found by solving the homogeneous system Ax = 0 using Gaussian elimination to obtain the reduced row echelon form, then identifying free variables.
The dimension of the null space is the number of free variables in the system, also known as the nullity of the matrix. It relates to the rank-nullity theorem.
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