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How to compute arccos for a matrix?

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Omar B.
Omar B. on 4 Jul 2020
Commented: Walter Roberson on 7 Jul 2020
I would like to compute the arccos for a matrix. I know when I want to find log(), exp(), and sqrt () for a matrix , we use logm(A), expm(A) and sqrtm(A) where A is a matrix.
I want to find the following:
x=acos(sqrtm(A)\eye(n))
so, Is it correct to compute it like this ? Or we need to use arccosm(sqrtm(A)\eye(n))? Thank you.
  2 Comments
Omar B.
Omar B. on 4 Jul 2020
So, is it correct to compute the following?
x=acos(sqrtm(A)\eye(n))

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Answers (1)

Walter Roberson
Walter Roberson on 5 Jul 2020
It depends what you are trying to calculate.
And so we could potentially generalize that for matrices, there might be some meaning to
arccosm = @(z) 1i * logm(z + sqrtm(z^2 - 1))
I am having difficulty thinking of a context in which there could be physical meaning for this.
If we substitute in 1/sqrtm(A) then
1i*logm(sqrtm(A\eye(n) - 1) + sqrtm(A)\eye(m))
But is there a meaning for this??
  11 Comments
Walter Roberson
Walter Roberson on 7 Jul 2020
f1 = @(x) acos(sqrtm(x)^(-1)) * sqrtm(x)^(-1);
f2 = @(x) acos(sqrtm(x)/eye(size(x,1))) / sqrtm(x);
f3 = @(x) acos(1./sqrt(x)) ./ sqrt(x);
f1(A)
f2(A)
f3(A)
Try them all and decide which one is the right solution for you.

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