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NullSpace

Usage

NullSpace[m]给出一个由矩阵m的零空间的基底构成的向量列表.


Notes

NullSpace既适用于数值矩阵,又适用于符号矩阵.
NullSpace[m, Modulus->n]给出整数矩阵模 n 的零空间.
NullSpace[m, ZeroTest -> test]test[ m[[i, j]] ] 进行计算以判断矩阵元素是否为零. 它的缺省设置是ZeroTest -> Automatic.
NullSpace中也可以给出Method可选项.可用的设置见LinearSolve.
• 参见Mathematica 全书: 3.7.8节.
• 同时参见: LinearSolve, RowReduce, SingularValues.
Further Examples

This matrix is nonsingular.

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The nullspace of a nonsingular matrix  is trivial. In other words, there is no nonzero vector  such that  .

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This nullspace has dimension  .

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This checks the result.

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These two vectors span the nullspace of the  x  matrix.

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Multiplying any linear combination of these vectors by the matrix gives the zero vector.

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This simplifies the expression.

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The rank of the matrix is the difference between the dimension of the range and the dimension of the nullspace.

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