Checking it during runtime would be fairly expensive although you might want to do it in debug builds to check that your assumptions hold. Note that whether or not the matrix is orthonormal is something that you should know from the analysis of the problem. Then computing the inverse of A is just a matter of subtracting the translation component, and multiplying by the transpose of the 3x3 part. Use WolframAlpha for viewing step-by-step methods and computing eigenvalues, eigenvectors, diagonalization and many other properties of square and non-square matrices. WolframAlpha is the perfect site for computing the inverse of matrices. its columns are orthonormal), then you can use the fact that inv(M) = transpose(M). More than just an online matrix inverse calculator. Where x is a 3x1 vector (usually a 3D point). Plouffe both before and during his period as an employee at CECM. The lookup tables include a substantial data set compiled by S. In that case, things simplify to inv(A) * = The Inverse Symbolic Calculator is an online number checker established Jby Peter Benjamin Borwein, Jonathan Michael Borwein and Simon Plouffe of the Canadian Centre for Experimental and Constructive Mathematics (Burnaby, Canada). The Inverse Symbolic Calculator (ISC) uses a combination of lookup tables and integer relation algorithms in order to associate a closed form representation with a user-defined, truncated decimal expansion (written as a floating point expression). The Inverse Symbolic Calculator is an online number checker established Jby Peter Benjamin Borwein, Jonathan Michael Borwein and Simon Plouffe of the Canadian Centre for Experimental and Constructive Mathematics (Burnaby, Canada). Where A is 4x4, M is 3x3, b is 3x1, and the bottom row is (0,0,0,1), then inv(A) = ĭepending on your situation, it may be faster to compute the result of inv(A) * x instead of actually forming inv(A). Namely, if your matrix looks like this A = You should be able to exploit the fact that the matrix is affine to speed things up over a full inverse.
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