> ## Documentation Index
> Fetch the complete documentation index at: https://docsa.stemfard.com/llms.txt
> Use this file to discover all available pages before exploring further.
# A guide to the Stemfard matrix operation endpoints
> Learn how to perform matrix arithmetic, element-wise operations, dimension queries, and statistical analysis using the Stemfard linear algebra endpoints.
The Stemfard API gives you a complete set of matrix operation endpoints under the `/api/v1/mathematics/linear-algebra/matrix-operations` path. This guide walks through every available category — arithmetic, element-wise operations, dimension queries, and statistics — and shows you concrete request and response examples so you can integrate them into your application quickly.
All endpoints accept an `api_level` parameter (`"lite"`, `"standard"`, or `"detailed"`) that controls how much solution detail the API returns alongside your result. See [API levels](/concepts/api-levels) for a full breakdown.
## Matrix arithmetic
Use the arithmetic endpoints to add, subtract, or multiply matrices. You can call the unified endpoint with an `operation` field, or use a dedicated sub-path for clarity.
**Supported `operation` values:** `"add"`, `"subtract"`, `"multiply-ew"`, `"divide-ew"`, `"raise-ew"`, `"matmul"`, `"all"`
### Addition
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2], [3, 4]],
"b": [[5, 6], [7, 8]],
"api_level": "lite",
"result_name": "sum"
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/add',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[1, 2], [3, 4]],
b: [[5, 6], [7, 8]],
api_level: 'lite',
result_name: 'sum',
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "sum",
"result": [[6, 8], [10, 12]],
"steps": null
}
```
### Subtraction
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[9, 8], [7, 6]],
"b": [[1, 2], [3, 4]],
"api_level": "lite",
"result_name": "diff"
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/subtract',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[9, 8], [7, 6]],
b: [[1, 2], [3, 4]],
api_level: 'lite',
result_name: 'diff',
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "diff",
"result": [[8, 6], [4, 2]],
"steps": null
}
```
### Matrix multiplication (matmul)
Matrix multiplication (dot product) requires the column count of `a` to equal the row count of `b`.
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2], [3, 4]],
"b": [[5, 6], [7, 8]],
"api_level": "lite",
"result_name": "product"
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/matmul',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[1, 2], [3, 4]],
b: [[5, 6], [7, 8]],
api_level: 'lite',
result_name: 'product',
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "product",
"result": [[19, 22], [43, 50]],
"steps": null
}
```
## Element-wise operations
Element-wise operations apply a function independently to each corresponding pair of elements across two matrices of the same shape. The matrices must have identical dimensions; no broadcasting is applied.
| Endpoint suffix | Operation | Description |
| --------------- | ------------------- | -------------------------------------------------- |
| `/multiply-ew` | `a[i][j] * b[i][j]` | Multiply each element by its counterpart |
| `/divide-ew` | `a[i][j] / b[i][j]` | Divide each element by its counterpart |
| `/raise-ew` | `a[i][j] ^ b[i][j]` | Raise each element to the power of its counterpart |
```bash element-wise multiply theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/multiply-ew \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2], [3, 4]],
"b": [[2, 3], [4, 5]],
"api_level": "lite",
"result_name": "ew_product"
}'
```
```bash element-wise divide theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/divide-ew \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[10, 20], [30, 40]],
"b": [[2, 4], [5, 8]],
"api_level": "lite",
"result_name": "ew_quotient"
}'
```
```bash element-wise power theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-arithmetic/raise-ew \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[2, 3], [4, 5]],
"b": [[3, 2], [2, 3]],
"api_level": "lite",
"result_name": "ew_power"
}'
```
**Sample response (multiply-ew)**
```json theme={null}
{
"result_name": "ew_product",
"result": [[2, 6], [12, 20]],
"steps": null
}
```
## Matrix dimensions
The dimension endpoints let you inspect the shape of any matrix without performing a computation. This is useful for validating input before passing matrices to arithmetic or statistics endpoints.
```bash shape theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-dimensions/shape \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2, 3], [4, 5, 6]],
"api_level": "lite"
}'
```
```bash row count theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-dimensions/nrows \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2, 3], [4, 5, 6]],
"api_level": "lite"
}'
```
```bash column count theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-dimensions/ncols \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2, 3], [4, 5, 6]],
"api_level": "lite"
}'
```
**Sample responses**
```json theme={null}
// shape
{ "result": [2, 3] }
// nrows
{ "result": 2 }
// ncols
{ "result": 3 }
```
## Matrix statistics
The statistics endpoints compute descriptive statistics across rows, columns, or the entire matrix. You can call the unified `/matrix-statistics` endpoint, or use a dedicated path for the specific statistic you need.
Available statistics: `row-min`, `col-min`, `mat-min`, `row-max`, `col-max`, `mat-max`, `row-sum`, `col-sum`, `mat-sum`, `row-mean`, `col-mean`, `mat-mean`, `row-median`, `col-median`, `mat-median`, `row-var`, `col-var`, `mat-var`, `row-std`, `col-std`, `mat-std`
### Row mean
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/row-mean \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[2, 4, 6], [1, 3, 5]],
"api_level": "lite",
"result_name": "row_means",
"decimals": 4
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/row-mean',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[2, 4, 6], [1, 3, 5]],
api_level: 'lite',
result_name: 'row_means',
decimals: 4,
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "row_means",
"result": [4.0, 3.0],
"steps": null
}
```
### Matrix sum
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/mat-sum \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[1, 2], [3, 4], [5, 6]],
"api_level": "lite",
"result_name": "total"
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/mat-sum',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[1, 2], [3, 4], [5, 6]],
api_level: 'lite',
result_name: 'total',
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "total",
"result": 21,
"steps": null
}
```
### Column standard deviation
```bash cURL theme={null}
curl --request POST \
--url https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/col-std \
--header 'Authorization: Bearer ' \
--header 'Content-Type: application/json' \
--data '{
"a": [[2, 4], [4, 8], [6, 12]],
"api_level": "lite",
"result_name": "col_stds",
"decimals": 4
}'
```
```javascript JavaScript theme={null}
const response = await fetch(
'https://api.stemfard.com/api/v1/mathematics/linear-algebra/matrix-operations/matrix-statistics/col-std',
{
method: 'POST',
headers: {
'Authorization': 'Bearer ',
'Content-Type': 'application/json',
},
body: JSON.stringify({
a: [[2, 4], [4, 8], [6, 12]],
api_level: 'lite',
result_name: 'col_stds',
decimals: 4,
}),
}
);
const data = await response.json();
```
**Sample response**
```json theme={null}
{
"result_name": "col_stds",
"result": [1.6330, 3.2660],
"steps": null
}
```