Trace Cf Minus 1 D90153
1. The problem is to find the trace of the matrix $CF - I$, where $C$ and $F$ are matrices and $I$ is the identity matrix.
2. Recall the definition of the trace: the trace of a matrix is the sum of its diagonal elements.
3. The trace of a difference of matrices is the difference of their traces: $$\text{trace}(CF - I) = \text{trace}(CF) - \text{trace}(I).$$
4. The trace of the identity matrix $I$ of size $n \times n$ is $n$ because all diagonal elements are 1.
5. Therefore, to find $\text{trace}(CF - I)$, you need to compute $\text{trace}(CF)$ and subtract $n$.
6. Without explicit matrices $C$ and $F$, the answer is expressed as $$\text{trace}(CF - I) = \text{trace}(CF) - n.$$