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PseudoInverse

Usage

PseudoInverse[m]求一个矩阵的伪逆。


Notes

PseudoInverse 对符号和数值矩阵都可以使用。
• 对数值矩阵,PseudoInverse[m, Tolerance -> t]指定去掉小于最大奇异值的t倍的奇异值。
• 缺省设置Tolerance -> Automatic 典型的取t为  ,其中p是输入的数值精度。
• 对非奇异方阵 ,伪逆 等于标准逆。
• 参见 Mathematica 全书: 3.7.10.
• 同时参见: Inverse, SingularValues, Fit.
• 相关包: LinearAlgebra`Cholesky`.
Further Examples

The pseudoinverse of a matrix m, usually denoted by  , has the property that the sum of the squares of the entries of  is minimized, where  is an identity matrix of the appropriate size.

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For invertible matrices, the pseudoinverse is the same as the inverse.

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Out[4]=

You can compute the pseudoinverse of a non-square matrix.

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Out[5]//MatrixForm=

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Out[6]//MatrixForm=

Here is another pseudoinverse.

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Out[7]//MatrixForm=

Here is another pseudoinverse. We use use Chop to get rid of the fuzz.

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Out[8]//MatrixForm=

We use use Chop to get rid of the fuzz.

In[9]:=  

Out[9]//MatrixForm=



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