How to calculate all the square roots of a matrix?

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Viswanath Hariharan
Viswanath Hariharan 2017-12-18
回答： Irshad Khan 2018-8-10
I have a matrix [5/8 3/8; 3/8 5/8] and it has more than one square root. If I perform sqrtm on it, it returns only one square root. How do I obtain all of its square roots?

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回答（2 个）

Walter Roberson
Walter Roberson 2017-12-19
x = sym('x', [2 2]);
xsq = x^2;
sol = solve(xsq == [5/8 3/8; 3/8 5/8]);
all_roots = arrayfun(@(x11, x12, x21, x22) [x11,x12;x21,x22], sol.x1_1, sol.x1_2, sol.x2_1, sol.x2_2, 'uniform', 0);
  2 个评论
Viswanath Hariharan
Viswanath Hariharan 2017-12-21
This did work. Thank you. But [-0.7071 -0.7071;-0.3536 0.3536] is also a root but this algorithm didn't find it out. Why so?
Walter Roberson
Walter Roberson 2017-12-22
T = sqrt(sym(2)); U = [-1/T -1/T;-1/T/2 1/T/2] double(U) %verify that U is the matrix you are talking about U^2
The result is
[ 3/4, 1/4]
[ 1/8, 3/8]
which is not your original matrix, so the matrix you indicate is not a square root of the original matrix.

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Irshad Khan
Irshad Khan 2018-8-10
How do I get only real roots?

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