Linear Algebra·orthogonal-projection

Orthogonal Projection

Calculate the orthogonal projection of a given vector onto a specified subspace defined by an orthogonal basis. Additionally, determine the distance from the vector to the subspace.

Math animationLinear Algebra · orthogonal-projection

✓ All 2 test cases pass.

Inputs

Vector y

The vector to be projected.

Basis vector u1

The first vector of the orthogonal basis.

Basis vector u2

The second vector of the orthogonal basis.

Test cases

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#	Inputs	Expected	Got	Status
1	{"vector_y":[1,1,0,0],"basis_u1":[1,0,1,0],"basis_u2":[0,1,0,1]}	0.5,0.5,0.5,0.5	0.5,0.5,0.5,0.5	✓
2	{"vector_y":[2,2,1,1],"basis_u1":[1,0,1,0],"basis_u2":[0,1,0,1]}	1.5,1.5,1.5,1.5	1.5,1.5,1.5,1.5	✓

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Endpoint

POST/api/calculators/linear-algebra/orthogonal-projection/compute

Inputs (3)

vector_yvectordefault [1,1,0,0]
basis_u1vectordefault [1,0,1,0]
basis_u2vectordefault [0,1,0,1]

Example

curl -sX POST http://localhost:3001/api/calculators/linear-algebra/orthogonal-projection/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"vector_y":[1,1,0,0],"basis_u1":[1,0,1,0],"basis_u2":[0,1,0,1]}}'

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: combinepdf.pdf. Reproduces a standard orthogonal-projection computation; problem text paraphrased.

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