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This is a bit of a variation on problem 1.7.2 from our text.
Let $A \in \mathbb R^{n\times n}$. How many multiplications are required to compute $A^8$?
Since A is a square matrix we can use the formula: $$\frac{(n^3)-n}{3}, n = 8$$ Which comes to 168
Edit: is this problem asking how many multiplications are needed to compute an n x n matrix by itself 8 times?
@dan Hmm... $n$ refers to the dimension of the matrix, not the matrix power. It's not 8; rather; it's unspecified so that your final answer should depend upon $n$.
Comments
Since A is a square matrix we can use the formula:
$$\frac{(n^3)-n}{3}, n = 8$$
Which comes to 168
Edit: is this problem asking how many multiplications are needed to compute an n x n matrix by itself 8 times?
@dan Hmm... $n$ refers to the dimension of the matrix, not the matrix power. It's not 8; rather; it's unspecified so that your final answer should depend upon $n$.