{"id":"matrix-multiply","version":"1.0.0","description":"Multiply an MxK finite-number matrix by a KxN finite-number matrix, producing an MxN matrix.","supported_operations":["matrix multiplication","matrix product","multiply two matrices"],"unsupported_operations":["elementwise multiplication (use matrix-hadamard)","incompatible inner dimensions","sparse matrix representation"],"semantics":["Input a is an MxK matrix and b is a KxN matrix of finite JSON numbers; a columns must equal b rows. M, K, N are each from 1 to 20.","Each entry magnitude is bounded to at most 1000000 before multiplication.","The result is the standard MxN matrix product, result[r][c] = sum over k of a[r][k] * b[k][c], accumulated left-to-right in IEEE-754 double precision.","A result entry of -0 is normalized to 0."],"limits":{"max_dim":20,"max_abs_value":1000000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["a","b"],"properties":{"a":{"type":"array","minItems":1,"maxItems":20,"items":{"type":"array","items":{"type":"number"}}},"b":{"type":"array","minItems":1,"maxItems":20,"items":{"type":"array","items":{"type":"number"}}}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result"],"properties":{"result":{"type":"array","items":{"type":"array","items":{"type":"number"}}}}},"examples":[{"input":{"a":[[1,2],[3,4]],"b":[[5,6],[7,8]]},"output":{"result":[[19,22],[43,50]]}}],"execute_url":"/v1/tools/matrix-multiply/versions/1.0.0/execute"}