NullSpace.md (749B)
1 # Null Space 2 3 Khan 4 5 **Definition:** The null space of matrix A is the set of vectors {$\vec{b} \in \R^n | \space \vec{b} \cdot A=\vec{0}$}. 6 7 These are all of the vectors that when multiplied by the matrix are equivalent to the zero vector. This is a closed ([Closure](Closure.md)) [Subspace](Subspace.md). 8 9 To calculate the null space do the following: 10 11 1. Get [Reduced Row Echelon Form](ReducedRowEchelonForm.md) 12 2. Write out find the values of each pivot entry (relation to other values) 13 3. Plug this into vectors of height n where each vector is multiplied by the corresponding axis component 14 15 The null set of a linearly independent set is always just the zero vector. This is an iff situation. 16 17 This is also sometimes referred to as the kernel.