{"id":"matrix-trace","version":"1.0.0","description":"Compute the trace (sum of diagonal entries) of a square finite-number matrix.","supported_operations":["matrix trace","sum of diagonal entries"],"unsupported_operations":["non-square matrices","generalized trace over a sub-diagonal"],"semantics":["Input matrix is a square NxN array of finite JSON numbers, N from 1 to 20, magnitude bounded to at most 1000000.","The result is the left-to-right IEEE-754 double-precision accumulation of matrix[i][i] for every diagonal index i.","A result 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":["matrix"],"properties":{"matrix":{"type":"array","minItems":1,"maxItems":20,"items":{"type":"array","items":{"type":"number"}}}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result"],"properties":{"result":{"type":"number"}}},"examples":[{"input":{"matrix":[[1,2],[3,4]]},"output":{"result":5}}],"execute_url":"/v1/tools/matrix-trace/versions/1.0.0/execute"}