We construct BPS states in the matrix description of M-theory. Startin
g from a set of basic M-theory branes, we study pair intersections whi
ch preserve supersymmetry. The fractions of the maximal supersymmetry
obtained in this way are 1/2, 1/4, 1/8, 3/16 and 1/16 In explicit exam
ples we establish that the matrix BPS states correspond to (intersecti
ng) brane configurations that are obtained from the d = 11 supersymmet
ry algebra. This correspondence for the 1/2 supersymmetric branes incl
udes the precise relations between the charges. (C) 1998 Elsevier Scie
nce B.V. All rights reserved.