Is there something wrong with the matrix-inversion function in J601v?
Remember that for any matrix z, the ranks of z and z'z are the same.
Here's some data:
1 1.058 1.11936 1.11936 1.18429 1.25298
1 1.088 1.18374 1.18374 1.28791 1.40125
1 1.086 1.1794 1.1794 1.28082 1.39097
1 1.122 1.25888 1.25888 1.41247 1.58479
1 1.186 1.4066 1.4066 1.66822 1.97851
1 1.254 1.57252 1.57252 1.97194 2.47281
1 1.246 1.55252 1.55252 1.93443 2.41031
1 1.232 1.51782 1.51782 1.86996 2.30379
1 1.298 1.6848 1.6848 2.18688 2.83856
1 1.37 1.8769 1.8769 2.57135 3.52275
1 1.439 2.07072 2.07072 2.97977 4.28789
1 1.479 2.18744 2.18744 3.23523 4.7849
1 1.474 2.17268 2.17268 3.20252 4.72052
1 1.503 2.25901 2.25901 3.39529 5.10312
1 1.475 2.17563 2.17563 3.20905 4.73334
read it into J as a numeric matrix, z.
Note that columns 2 and 3 are identical.
Now compute:
mp =. +/ . * NB. matrix product
zp =. |: z NB. transpose
zpz =. zp mp z NB. z'z
Since this does not have full rank, the inverse matrix
does not exist. But
%. zpz
produces a result. Why? I read my matrix z into
a statistics package and went through the same steps
there: the package refused to compute the inverse
reporting (correctly) that the matrix was singular.
The Dictionary page for %. says that for a non-singular
matrix, mondaic %. computes the inverse. There's no
mention of what happens if the matrix is singular; one
would assume that some sort of failure would be reported, no?
------------------------
Philip A. Viton
City Planning, Ohio State University
275 West Woodruff Avenue, Columbus OH 43210
[EMAIL PROTECTED]
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