Spacetime addition

Add4[A_, B_] := Plus[A, B]

Add4[a4, b4]//MatrixForm

( {{a0 + b0}, {{at + bt, ax + bx, ay + by, az + bz}}, {{atx + btx, aty + bty, atz + ... xy, ayz + byx, azx + bzx}}, {{ait + bit, aix + bix, aiy + biy, aiz + biz}}, {ai + bi}} )

Add4[a4v, b4v]//MatrixForm

( {{0}, {{at + bt, ax + bx, ay + by, az + bz}}, {{0, 0, 0, 0, 0, 0}}, {{0, 0, 0, 0}}, {0}} )

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