{"id":"matrix-vector-multiply","version":"1.0.0","description":"Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.","supported_operations":["matrix-vector multiplication","apply a matrix to a vector","linear transformation"],"unsupported_operations":["vector-matrix multiplication on the left (transpose the matrix first)","mismatched dimensions"],"semantics":["Input matrix is an MxN matrix of finite JSON numbers (M, N from 1 to 20). Input vector has exactly N finite JSON number entries.","Each entry magnitude is bounded to at most 1000000.","The result is the length-M vector result[r] = sum over c of matrix[r][c] * vector[c], accumulated left-to-right in IEEE-754 double precision.","A result entry of -0 is normalized to 0."],"limits":{"max_matrix_dim":20,"max_vector_dim":64,"max_abs_value":1000000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["matrix","vector"],"properties":{"matrix":{"type":"array","minItems":1,"maxItems":20,"items":{"type":"array","items":{"type":"number"}}},"vector":{"type":"array","minItems":1,"maxItems":20,"items":{"type":"number"}}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result"],"properties":{"result":{"type":"array","items":{"type":"number"}}}},"examples":[{"input":{"matrix":[[1,2],[3,4]],"vector":[5,6]},"output":{"result":[17,39]}}],"execute_url":"/v1/tools/matrix-vector-multiply/versions/1.0.0/execute"}