Math Is Fun Forum

White_Owl

Member

Registered: 2010-03-03

Posts: 106

Linear transformation from R^{3x3} to R

We have a linear transformation from a matrix space, to a real space defined as a product of all elements in the matrix.
How can we define a matrix representing such transformation with respect to the standard basis?

The 'standard basis' here is a set of matrices:

But the result is not a matrix.

So I can write something like that:

But how to define a matrix representing such transformation?

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Linear transformation from R^{3x3} to R

We have a linear transformation from a matrix space, to a real space defined as a product of all elements in the matrix.

No, we don’t. Such a mapping is not a linear transformation. Example: Let A be the matrix with all entries 1; then A+A is the matrix with all entries 2. However

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so the additivity property of a linear transformation is violated. Hence T is not a linear transformation.

Last edited by Olinguito (2014-08-14 12:08:14)

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