Linear Algebra·distance-to-subspace

Distance To Subspace

Determine the distance from a vector to a subspace defined by an orthogonal basis, using the projection calculated previously.

Math animationLinear Algebra · distance-to-subspace

✓ All 2 test cases pass.

Inputs

Vector y

The vector from which the distance is measured.

Projected vector

The orthogonal projection of the vector onto the subspace.

Test cases

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#	Inputs	Expected	Got	Status
1	{"vector_y":[1,1,0,0],"projected_y":[0.5,0.5,0,0.5]}	0.866025	0.8660254037844386	✓
2	{"vector_y":[2,2,1,1],"projected_y":[1,1,0.5,0.5]}	1.581139	1.5811388300841898	✓

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Endpoint

POST/api/calculators/linear-algebra/distance-to-subspace/compute

Inputs (2)

vector_yvectordefault [1,1,0,0]
projected_yvectordefault [0.5,0.5,0,0.5]

Example

curl -sX POST http://localhost:3001/api/calculators/linear-algebra/distance-to-subspace/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"vector_y":[1,1,0,0],"projected_y":[0.5,0.5,0,0.5]}}'

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: combinepdf.pdf. Reproduces a standard distance-to-subspace computation; problem text paraphrased.

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