Question

Let CL(n,R) be the multiplicative group of invertible nxn matrices, and let R be the additive group of real numbers. Let ф:CL(n,R) R be given by ф(A)=tr(A), where tr(A) is defined is defined in Exercise 13 .

Answer 1

CL(n,R) is the multiplicative group of invertible nxn matrices, R is the additive group of real numbers, and φ(A) = tr(A) with tr(A) being the sum of the diagonal elements of matrix A.

Step-by-step explanation:

Multiplicative Group and Additive Group:

CL(n,R) is the multiplicative group of invertible nxn matrices and R is the additive group of real numbers. In this context, the term 'group' refers to a set of elements with an operation that satisfies certain properties.

The Function φ:

The function φ maps the elements of CL(n,R) to real numbers by taking the trace (tr) of a matrix. 'tr(A)' represents the sum of the diagonal elements of matrix A.