{"id":"matrix-inverse","version":"1.0.0","description":"Compute the inverse of a small square finite-number matrix.","supported_operations":["matrix inverse","invert a square matrix"],"unsupported_operations":["non-square matrices","matrices larger than 12x12","pseudo-inverse of a singular or non-square matrix"],"semantics":["Input matrix is a square NxN array of finite JSON numbers, N from 1 to 12, magnitude bounded to at most 1000000.","Computed via Gauss-Jordan elimination with partial (largest-magnitude) pivoting in IEEE-754 double precision.","Optional input tolerance (default 1e-9, range 0 to 1) is the minimum acceptable pivot magnitude; if every remaining candidate pivot in a column is at or below tolerance, the matrix is rejected as singular or numerically singular.","Results for small integer-valued invertible matrices are typically exact; floating-point rounding can appear for larger or ill-conditioned matrices.","A result entry of -0 is normalized to 0.","Every result entry is checked to be a finite number before it is returned; a very small nonzero pivot (below tolerance-rejection but large enough to be accepted) can otherwise amplify through elimination to overflow, which is rejected as invalid input rather than silently serialized as null."],"limits":{"max_dim":12,"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":12,"items":{"type":"array","items":{"type":"number"}}},"tolerance":{"type":"number","minimum":0,"maximum":1}}},"output_schema":{"type":"object","additionalProperties":false,"required":["result"],"properties":{"result":{"type":"array","items":{"type":"array","items":{"type":"number"}}}}},"examples":[{"input":{"matrix":[[2,0],[0,4]]},"output":{"result":[[0.5,0],[0,0.25]]}}],"execute_url":"/v1/tools/matrix-inverse/versions/1.0.0/execute"}