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Matrices (and also vectors and other tensors) are multipled using Dot. Using your code, just replace * by . (I also removed all ('s and )'s as they don't do anything in this context. {{x, y, 1}}.{{a, b/2, d/2}, {b/2, c, e/2}, {d/2, e/2, f}}.{{x}, {y}, {1}} Result:


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For the love of this fine site, please post copyable code along with accompanying images the next time! Anyway: myb1 = {{{{1, 2}, {1, 2}}, {{2, 3}, {3, 4}}}, {{{5, 2}, {8, 2}}, {{1, 2}, {1, 2}}}}; Map[MatrixPower[#, 2] &, myb1, {2}] {{{{3, 6}, {3, 6}}, {{13, 18}, {18, 25}}}, {{{41, 14}, {56, 20}}, {{3, 6}, {3, 6}}}} Map[#.# &, ...


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In general, the relation between an original matrix and the eigenvalue decomposition is the following: m = RandomReal[1, {5, 5}]; {eval, evec} = Eigensystem[m]; Norm[Transpose[evec].DiagonalMatrix[eval].Inverse@Transpose[evec]-m] which outputs 0. So, in order to diagonalize the matrix m, we have to evaluate Inverse[u].m.u with u=Tranpose@Eigenvectors@m.



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