sqrtm
Matrix square root
Description
Examples
Compute Square Root of Matrix
Compute the square root of this matrix. Because these numbers are not symbolic objects, you get floating-point results.
A = [2 -2 0; -1 3 0; -1/3 5/3 2]; X = sqrtm(A)
X = 1.3333 -0.6667 0.0000 -0.3333 1.6667 -0.0000 -0.0572 0.5286 1.4142
Now, convert this matrix to a symbolic object, and compute its square root again:
A = sym([2 -2 0; -1 3 0; -1/3 5/3 2]); X = sqrtm(A)
X = [ 4/3, -2/3, 0] [ -1/3, 5/3, 0] [ (2*2^(1/2))/3 - 1, 1 - 2^(1/2)/3, 2^(1/2)]
Check the correctness of the result:
isAlways(X^2 == A)
ans = 3×3 logical array 1 1 1 1 1 1 1 1 1
Return Residual of Matrix Square Root
Use the syntax with two output arguments to return the square root of a matrix and the residual:
A = vpa(sym([0 0; 0 5/3]), 100); [X,resnorm] = sqrtm(A)
X = [ 0, 0] [ 0, 1.2909944487358056283930884665941] resnorm = 2.9387358770557187699218413430556e-40
Input Arguments
Output Arguments
Tips
Calling
sqrtm
for a matrix that is not a symbolic object invokes the MATLAB®sqrtm
function.
Version History
Introduced in R2013a