Null Space

Null Space

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If $\it{T}$ is a linear transformation of \mathbb{R}^n, then the null space Null($\it{T}$), also called the kernel $\it{Ker(T)}$, is the set of all vectors $\it{X}$ such that

i.e.,

The term "null space" is most commonly written as two separate words (e.g., Golub and Van Loan 1989, pp. 49 and 602; Zwillinger 1995, p. 128), although other authors write it as a single word "nullspace" (e.g., Anton 1994, p. 259; Robbin 1995, pp. 123 and 180).

Each null space vector corresponds to a zero eigenvector of the transformation matrix of $\it{T}$.