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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

​
a
number[][]
required
The first input matrix, expressed as an array of row arrays. Default: [[5, 1, 6], [3, 4, 5], [6, 4, 8]].
​
b
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]].
​
operation
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
​
result_name
string
default:"ans"
Name assigned to the computed result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
steps_bg
boolean
default:"true"
Include background theory alongside solution steps.
​
steps_output_formats
string[]
default:"[\"\"]"
Format for step content: "html", "latex", or "speech".
​
decimals
integer | null
default:"null"
Decimal precision for rounding the result. Pass null for full precision.
​
apply_decimals_in_steps
boolean
default:"false"
Apply decimals rounding to intermediate step values.
​
request_params
boolean
default:"true"
Include normalized request parameters in the response.
​
learning_pathways
boolean
default:"true"
Include curated learning resource links in the response.
​
related
boolean
default:"true"
Include links to related Stemfard endpoints in the response.
​
properties
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"
  }'
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.
Adds two matrices element by element. a and b must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add
​
a
number[][]
required
First input matrix.
​
b
number[][]
required
Second input matrix. Must have the same dimensions as a.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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"
  }'
200
{
  "sum": [[8, 10, 12], [14, 16, 18]]
}
Subtracts b from a element by element. Both matrices must have identical dimensions.POST /api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract
​
a
number[][]
required
First input matrix (minuend).
​
b
number[][]
required
Second input matrix (subtrahend). Must have the same dimensions as a.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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"
  }'
200
{
  "difference": [[9, 15], [20, 25]]
}
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
​
a
number[][]
required
First input matrix.
​
b
number[][]
required
Second input matrix. Must have the same dimensions as a.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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"
  }'
200
{
  "hadamard": [[5, 12], [21, 32]]
}
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
​
a
number[][]
required
Numerator matrix.
​
b
number[][]
required
Denominator matrix. Must have the same dimensions as a. No element may be zero.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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
  }'
200
{
  "quotient": [[5.0, 5.0], [6.0, 5.0]]
}
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
​
a
number[][]
required
Base matrix.
​
b
number[][]
required
Exponent matrix. Must have the same dimensions as a.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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"
  }'
200
{
  "power": [[8, 9], [16, 125]]
}
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
​
a
number[][]
required
Left-hand matrix. An m × k matrix.
​
b
number[][]
required
Right-hand matrix. A k × n matrix. The number of rows must equal the number of columns in a.
​
result_name
string
default:"ans"
Name for the result in the response.
​
api_level
string
default:"detailed"
Response verbosity: "lite", "standard", or "detailed".
​
decimals
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"
  }'
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.