Linear Algebra·eigenspace-basis

Eigenspace Basis

For a given matrix A and a specified eigenvalue, determine the basis for the eigenspace associated with that eigenvalue by solving the corresponding homogeneous system.

✓ All 2 test cases pass.

Inputs

Matrix A

An n x n matrix for which the eigenspace is to be found.

Eigenvalue

The eigenvalue corresponding to the eigenspace.

Test cases

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#	Inputs	Expected	Got	Status
1	{"matrix_a":[[-1,2,0],[0,1,1],[0,4,1]],"eigenvalue":-1}	1,0,0	1,0,0	✓
2	{"matrix_a":[[4,4,-2],[1,4,-1],[3,6,-1]],"eigenvalue":2}	2,-1,0,1,0,1	2,-1,0,1,0,1	✓

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Endpoint

POST/api/calculators/linear-algebra/eigenspace-basis/compute

Inputs (2)

matrix_amatrixdefault [[1,0],[0,1]]
eigenvaluenumberdefault 1

Example

curl -sX POST http://localhost:3001/api/calculators/linear-algebra/eigenspace-basis/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"matrix_a":[[1,0],[0,1]],"eigenvalue":1}}'

Try it live

Edit the body below, then click Call API.

Request body

Response

(click Call API to see the response)

full API docs →

Source: Pattern from: Test 2-08 Version B (Solution).pdf. Reproduces a standard eigenspace-basis computation; problem text paraphrased.

AI disclosure: Calculator code generated by openai/gpt-4o-mini-2024-07-18; verified by 2 test cases.