What mistake did I make in this matrix multiplication in Julia? -


in julia:

in  [1]: m1 = [1 3 4;               45 64 33;               456 3 454;]  out [1]: 3x3 array{int64,2}:    1   3    4   45  64   33  456   3  454  in  [2]: m1 * inv(m1)  out [2]: 3x3 array{float64,2}:   1.0           6.93889e-18  -8.67362e-19   0.0           1.0          -2.08167e-17  -1.42109e-14  -8.88178e-16   1.0

m1 * inv(m1) supposed identity matrix definition. what's wrong?

i tried same thing in matlab:

>> m1 = [1 3 4;          45 64 33;         456 3 454;] m1 =      1     3     4     45    64    33    456     3   454 >> inv(m1) ans =   -0.280088987764182   0.013057987135465   0.001518595540939    0.052057842046719   0.013251438796731  -0.001421869710306    0.280978865406007  -0.013203075881414   0.000686753397495 >> m1 * inv(m1) ans =    1.000000000000000   0.000000000000000  -0.000000000000000                    0   1.000000000000000  -0.000000000000000   -0.000000000000014  -0.000000000000001   1.000000000000000 >>

matlab returns right result here. guess julia not make mistake here. what's wrong calculation / notation?

edit

the problem caused number of digits in floating point result. should have asked, how set result digits precision in julia?

julia , matlab give same result (for instance, bottom-left element -1.4e-14 in both cases): not identity matrix because floating point arithmetic not exact.

you can explicitly round result before displaying it.

m1 = [   1    3   4;   45  64  33;   456  3 454 ] round( m1 * inv(m1), 6 ) # 3x3 array{float64,2}: #  1.0   0.0  -0.0 #  0.0   1.0  -0.0 #  0.0  -0.0   1.0

if want exact result, can use rationals.

m1 = [   1//1  3   4;   45   64  33;   456   3 454 ] m1 * inv(m1) # 3x3 array{rational{int64},2}: #  1//1  0//1  0//1 #  0//1  1//1  0//1 #  0//1  0//1  1//1

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