Subspace Properties
The null space of an m × n matrix is a subspace of Rn. That is, the set Null(A) has the following three properties:
- Null(A) always contains the zero vector, since A0 = 0.
- If x ∈ Null(A) and y ∈ Null(A), then x + y ∈ Null(A). This follows from the distributivity of matrix multiplication over addition.
- If x ∈ Null(A) and c is a scalar, then c x ∈ Null(A), since (cA)x = c(Ax).
Read more about this topic: Kernel (matrix)
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