See http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html

d65 white
 0.950470 1.000000 1.088830
 [ xws yws zws ]

d50 white
 0.964220 1.000000 0.825210
 [ xwd ywd zwd ] 

 0.941429 1.040417 1.089533
 [ as bs cs] = [ xws yws zws ] [ Bradford ]

 0.996284 1.020427 0.818644
 [ ad bd cd] = [ xwd ywd zwd ] [ Bradford ]

 1.058269 0.000000 0.000000
 0.000000 0.980786 0.000000
 0.000000 0.000000 0.751372
           [ ad/as   0     0   ]
matrix c = [ 0     bd/bs   0   ]
           [ 0       0   cd/cs ]

d65->d50 chromatic adaptation matrix (Bradford Method)
 1.047811 0.029542 -0.009235
 0.022887 0.990484 0.015044
 -0.050127 -0.017049 0.752132
cam = [ Bradford] c [ inverseof( Bradford ) ]

sRGB (d65)
 0.412424 0.212656 0.019332
 0.357579 0.715158 0.119193
 0.180464 0.072186 0.950444
 = srgb_d65

adapted sRGB (d50)
 0.436040 0.222487 0.013931
 0.385068 0.716884 0.097105
 0.143102 0.060626 0.714279
 srgb_d50 = srgb_d65 [ cam ]