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01-20-2000
03:00 AM

01-20-2000
03:00 AM

Matrix Norms

Every where I've looked, for a matrix, the Euclidean norm and 2-norm are defined as the same. Yet Mathcad has to different functions for this particular norm, and both yield different results [norm2() and norme()]. Am I missing something simple?

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01-21-2000
03:00 AM

01-21-2000
03:00 AM

Matrix Norms

The "2-norm" is the matrix norm that is *induced* from

n-dimensional space with the usual Euclidean norm: see

http://www.eece.unm.edu/faculty/chaouki/COURSES/EECE595/review595/node4.html

for example. norm2(A) = 4.4576

The "Euclidean norm" (also called the "Frobenius norm")

is simply the root sum of squares of matrix elements.

The Mathcad terminology is consistent with Matlab's,

for example:

http://www.eng.uc.edu/occ/newdocs/matlab.51/techdoc/ref/norm.html

Hope that helps.

n-dimensional space with the usual Euclidean norm: see

http://www.eece.unm.edu/faculty/chaouki/COURSES/EECE595/review595/node4.html

for example. norm2(A) = 4.4576

The "Euclidean norm" (also called the "Frobenius norm")

is simply the root sum of squares of matrix elements.

The Mathcad terminology is consistent with Matlab's,

for example:

http://www.eng.uc.edu/occ/newdocs/matlab.51/techdoc/ref/norm.html

Hope that helps.