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I don't know how to convert $xyz$ chromaticity coordinates in sRGB. For example in What {R,G,B} values would represent a 445nm monochrome lightsource color on a computer monitor? the author takes:

$$xyz = (0.145945, 0.045217, 0.808838) \rightarrow RGB = (1.47450, -178.21694, 345.59392)$$

But when I use the transfer matrix cited on wikipedia (https://en.wikipedia.org/wiki/SRGB) I find:

$$xyz = (0.145945, 0.045217, 0.808838) \rightarrow RGB = (0.000155,-0.023021, 0.854036)$$ In 8 bit, I have $RGB =(0.04,-5.9,217.8)$. So, it's very différent!

Is it possible to explain step by step to detect my mistake?

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closed as off-topic by Kyle Kanos, Jon Custer, GiorgioP, Feynmans Out for Grumpy Cat, ZeroTheHero Mar 9 at 1:13

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    $\begingroup$ FWIW: The colors of many (most?) pure monochrome light sources lie outside of the color gamut of an RGB monitor. What you're actually looking for is the RGB triplet most closely approximates the color of the given pure wavelength. The colors that a monitor can reproduce, in general will be slightly less saturated than pure monochrome colors. $\endgroup$ – Solomon Slow Mar 7 at 14:23