Stemfard matrix arithmetic API endpoints reference

The matrix arithmetic endpoints let you perform basic arithmetic operations on matrices. There are seven endpoints in this group: a combined endpoint that accepts an operation parameter, and six individual endpoints — one per operation. All endpoints accept two input matrices a and b (or a and a scalar for element-wise operations) and the full set of common request parameters.

Combined endpoint

Use this endpoint to run any arithmetic operation in a single request by setting the operation field. POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic

Parameters

number[][]

required

The first input matrix, expressed as an array of row arrays. Default: [[5, 1, 6], [3, 4, 5], [6, 4, 8]].

number[][] | number

required

The second input matrix or scalar. For element-wise operations, b must have the same dimensions as a. For matmul, the number of columns in a must equal the number of rows in b. Default: [[-4, -2, 6], [4, 7, -3], [7, -3, 5]].

string

required

The arithmetic operation to perform. Accepted values:

"all" — run all operations and return all results
"add" — element-wise addition
"subtract" — element-wise subtraction
"multiply-ew" — element-wise (Hadamard) multiplication
"divide-ew" — element-wise division
"raise-ew" — element-wise power (each element of a raised to the corresponding element of b)
"matmul" — standard matrix multiplication

string

default:"ans"

Name assigned to the computed result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

boolean

default:"true"

Include background theory alongside solution steps.

string[]

default:"[\"\"]"

Format for step content: "html", "latex", or "speech".

integer | null

default:"null"

Decimal precision for rounding the result. Pass null for full precision.

boolean

default:"false"

Apply decimals rounding to intermediate step values.

boolean

default:"true"

Include normalized request parameters in the response.

boolean

default:"true"

Include curated learning resource links in the response.

Include links to related Stemfard endpoints in the response.

boolean

default:"true"

Include a description of the result object’s properties.

Example — matrix multiplication via the combined endpoint

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
    "b": [[1, 0], [0, 1], [2, 3]],
    "operation": "matmul",
    "result_name": "product",
    "api_level": "standard"
  }'

const response = await fetch(
  'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic',
  {
    method: 'POST',
    headers: {
      'Authorization': 'Bearer <your-api-key>',
      'Content-Type': 'application/json',
    },
    body: JSON.stringify({
      a: [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
      b: [[1, 0], [0, 1], [2, 3]],
      operation: 'matmul',
      result_name: 'product',
      api_level: 'standard',
    }),
  }
);
const data = await response.json();

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic',
    headers={
        'Authorization': 'Bearer <your-api-key>',
        'Content-Type': 'application/json',
    },
    json={
        'a': [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
        'b': [[1, 0], [0, 1], [2, 3]],
        'operation': 'matmul',
        'result_name': 'product',
        'api_level': 'standard',
    },
).json()

200

{
  "product": [[8, 16], [16, 17], [11, 17]],
  "operation": "matmul"
}

Individual operation endpoints

Each operation has its own focused endpoint. These endpoints do not accept an operation field — the operation is determined by the path. All accept a, b, and the common parameters.

POST .../matrix-arithmetic/add — element-wise addition

Adds two matrices element by element. a and b must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add

number[][]

required

First input matrix.

number[][]

required

Second input matrix. Must have the same dimensions as a.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[1, 2, 3], [4, 5, 6]],
    "b": [[7, 8, 9], [10, 11, 12]],
    "result_name": "sum",
    "api_level": "standard"
  }'

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[1, 2, 3], [4, 5, 6]],
        'b': [[7, 8, 9], [10, 11, 12]],
        'result_name': 'sum',
        'api_level': 'standard',
    },
).json()

200

{
  "sum": [[8, 10, 12], [14, 16, 18]]
}

POST .../matrix-arithmetic/subtract — element-wise subtraction

Subtracts b from a element by element. Both matrices must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract

number[][]

required

First input matrix (minuend).

number[][]

required

Second input matrix (subtrahend). Must have the same dimensions as a.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[10, 20], [30, 40]],
    "b": [[1, 5], [10, 15]],
    "result_name": "difference",
    "api_level": "lite"
  }'

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[10, 20], [30, 40]],
        'b': [[1, 5], [10, 15]],
        'result_name': 'difference',
        'api_level': 'lite',
    },
).json()

200

{
  "difference": [[9, 15], [20, 25]]
}

POST .../matrix-arithmetic/multiply-ew — element-wise multiplication

Computes the Hadamard (element-wise) product of a and b. Each element at position (i, j) in the result equals a[i][j] × b[i][j]. Both matrices must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/multiply-ew

number[][]

required

First input matrix.

number[][]

required

Second input matrix. Must have the same dimensions as a.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/multiply-ew \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[1, 2], [3, 4]],
    "b": [[5, 6], [7, 8]],
    "result_name": "hadamard",
    "api_level": "lite"
  }'

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/multiply-ew',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[1, 2], [3, 4]],
        'b': [[5, 6], [7, 8]],
        'result_name': 'hadamard',
        'api_level': 'lite',
    },
).json()

200

{
  "hadamard": [[5, 12], [21, 32]]
}

POST .../matrix-arithmetic/divide-ew — element-wise division

Divides each element of a by the corresponding element of b. Both matrices must have identical dimensions. Division by zero in b will produce an error.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/divide-ew

number[][]

required

Numerator matrix.

number[][]

required

Denominator matrix. Must have the same dimensions as a. No element may be zero.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/divide-ew \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[10, 20], [30, 40]],
    "b": [[2, 4], [5, 8]],
    "result_name": "quotient",
    "api_level": "lite",
    "decimals": 2
  }'

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/divide-ew',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[10, 20], [30, 40]],
        'b': [[2, 4], [5, 8]],
        'result_name': 'quotient',
        'api_level': 'lite',
        'decimals': 2,
    },
).json()

200

{
  "quotient": [[5.0, 5.0], [6.0, 5.0]]
}

POST .../matrix-arithmetic/raise-ew — element-wise power

Raises each element of a to the power of the corresponding element of b. The result at position (i, j) equals a[i][j] ^ b[i][j]. Both matrices must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/raise-ew

number[][]

required

Base matrix.

number[][]

required

Exponent matrix. Must have the same dimensions as a.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/raise-ew \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[2, 3], [4, 5]],
    "b": [[3, 2], [2, 3]],
    "result_name": "power",
    "api_level": "lite"
  }'

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/raise-ew',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[2, 3], [4, 5]],
        'b': [[3, 2], [2, 3]],
        'result_name': 'power',
        'api_level': 'lite',
    },
).json()

200

{
  "power": [[8, 9], [16, 125]]
}

POST .../matrix-arithmetic/matmul — matrix multiplication

Performs standard matrix multiplication (dot product). The number of columns in a must equal the number of rows in b. If a is m × k and b is k × n, the result is m × n.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul

number[][]

required

Left-hand matrix. An m × k matrix.

number[][]

required

Right-hand matrix. A k × n matrix. The number of rows must equal the number of columns in a.

string

default:"ans"

Name for the result in the response.

string

default:"detailed"

Response verbosity: "lite", "standard", or "detailed".

integer | null

default:"null"

Decimal precision for the result.

Example

curl --request POST \
  --url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul \
  --header 'Authorization: Bearer <your-api-key>' \
  --header 'Content-Type: application/json' \
  --data '{
    "a": [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
    "b": [[1, 0], [0, 1], [2, 3]],
    "result_name": "product",
    "api_level": "standard"
  }'

const response = await fetch(
  'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul',
  {
    method: 'POST',
    headers: {
      'Authorization': 'Bearer <your-api-key>',
      'Content-Type': 'application/json',
    },
    body: JSON.stringify({
      a: [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
      b: [[1, 0], [0, 1], [2, 3]],
      result_name: 'product',
      api_level: 'standard',
    }),
  }
);
const data = await response.json();

import requests

data = requests.post(
    'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul',
    headers={'Authorization': 'Bearer <your-api-key>', 'Content-Type': 'application/json'},
    json={
        'a': [[2, 7, 3], [4, -1, 6], [5, 8, 3]],
        'b': [[1, 0], [0, 1], [2, 3]],
        'result_name': 'product',
        'api_level': 'standard',
    },
).json()

200

{
  "product": [[8, 16], [16, 17], [11, 17]]
}

Matrix multiplication is not commutative — a × b is not equal to b × a in general. Make sure you pass the matrices in the correct order for your use case.

Overview

Linear Algebra

Stemfard matrix arithmetic API endpoints reference

Combined endpoint

Parameters

Example — matrix multiplication via the combined endpoint

Individual operation endpoints

​Combined endpoint

​Parameters

​Example — matrix multiplication via the combined endpoint

​Individual operation endpoints

Combined endpoint

Parameters

Example — matrix multiplication via the combined endpoint

Individual operation endpoints