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December 31 Information
Matrices and Indices
Can you raise a number to the power of a matrix and if so how?
By defining some arbitrary function on a number and a matrix and calling it a power. ...But more seriously, take a look at
matrix exponential. I can think of at least one immediate generalization of this to arbitrary real or complex bases. «
Aaron Rotenberg «
Talk « 02:09, 31 December 2012 (UTC)reply
If a>0 and M is a square matrix, then aM= eM log(a). If a is not a positive real then log(a) is multivalued.
Bo Jacoby (
talk) 05:30, 31 December 2012 (UTC).reply
So once you've worked out log(a) and multiplied it by M, how do you then raise e to the power of that? — Preceding
unsigned comment added by
86.151.178.51 (
talk) 14:25, 31 December 2012 (UTC)reply
Bo, in the last expression, is "1" supposed to be the identity matrix "I"? Otherwise it's adding a scalar 1 to a matrix M/n. Is there a reference for this expression with the identity matrix?--if so, it's a nice intuitive generalization of the scalar formula, and I suggest you put it into the
matrix exponential article.
Duoduoduo (
talk) 12:30, 2 January 2013 (UTC)reply
Mathematicians often use 1 to denote the identity matrix, or more generally the identity in any algebra over a field. There is no risk of confusion, since an algebra contains an isomorphic copy of its field of scalars, so it is natural to identify the scalars with multiples of the identity. This practice is very widespread.
Sławomir Biały (
talk) 13:12, 2 January 2013 (UTC)reply
Okay. Could someone provide a link to a citation for Bo's last formula above, so I can put it into the article?
Duoduoduo (
talk) 14:17, 2 January 2013 (UTC)reply
Also, in the above-referenced article
matrix exponential, see the sections "Computing the matrix exponential" and "Calculations".
Duoduoduo (
talk) 15:39, 31 December 2012 (UTC)reply
Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is a
transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the
current reference desk pages.
December 31 Information
Matrices and Indices
Can you raise a number to the power of a matrix and if so how?
By defining some arbitrary function on a number and a matrix and calling it a power. ...But more seriously, take a look at
matrix exponential. I can think of at least one immediate generalization of this to arbitrary real or complex bases. «
Aaron Rotenberg «
Talk « 02:09, 31 December 2012 (UTC)reply
If a>0 and M is a square matrix, then aM= eM log(a). If a is not a positive real then log(a) is multivalued.
Bo Jacoby (
talk) 05:30, 31 December 2012 (UTC).reply
So once you've worked out log(a) and multiplied it by M, how do you then raise e to the power of that? — Preceding
unsigned comment added by
86.151.178.51 (
talk) 14:25, 31 December 2012 (UTC)reply
Bo, in the last expression, is "1" supposed to be the identity matrix "I"? Otherwise it's adding a scalar 1 to a matrix M/n. Is there a reference for this expression with the identity matrix?--if so, it's a nice intuitive generalization of the scalar formula, and I suggest you put it into the
matrix exponential article.
Duoduoduo (
talk) 12:30, 2 January 2013 (UTC)reply
Mathematicians often use 1 to denote the identity matrix, or more generally the identity in any algebra over a field. There is no risk of confusion, since an algebra contains an isomorphic copy of its field of scalars, so it is natural to identify the scalars with multiples of the identity. This practice is very widespread.
Sławomir Biały (
talk) 13:12, 2 January 2013 (UTC)reply
Okay. Could someone provide a link to a citation for Bo's last formula above, so I can put it into the article?
Duoduoduo (
talk) 14:17, 2 January 2013 (UTC)reply
Also, in the above-referenced article
matrix exponential, see the sections "Computing the matrix exponential" and "Calculations".
Duoduoduo (
talk) 15:39, 31 December 2012 (UTC)reply