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**A multidimensional array** is a data structure where elements are organized **across several dimensions** (rows, columns, levels, etc.), that is, an array *made up of other arrays*.

In simpler terms, it's a way to store data **as a table, a matrix, or a cube**, rather than a single long line.

---

### **1. Example of a two-dimensional array**

A two-dimensional array can be pictured as a table:

```javascript
A = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
]
```

Here:

- `A[0][0] = 1`
- `A[1][2] = 6`
- `A[2][1] = 8`

This is an array of 3 rows and 3 columns.

---

### **2. Three-dimensional array**

Can be pictured as a "data cube":

```javascript
B[x][y][z]
```

Example: `B[2][1][0]` is the element from the third layer, second row, first column.

---

### **3. Storage in memory**

Even though visually this is a "table" or a "cube",
in memory a multidimensional array is stored **as a single contiguous sequence of elements**.

There are two main placement methods:

- **Row-major order**: by rows (C, C++, Python)
- **Column-major order**: by columns (Fortran, MATLAB)

For example, for a 3×3 two-dimensional array, the elements `[ [1,2,3], [4,5,6], [7,8,9] ]` are stored one after another:

```javascript
1, 2, 3, 4, 5, 6, 7, 8, 9
```

---

### **4. Formula for an element's address**

For a two-dimensional array with `n` columns:

[
\text{address}(A[i][j]) = \text{base_address} + ((i \times n) + j) \times \text{size}
]

Where:

- `i` is the row number,
- `j` is the column number,
- `size` is the size of one element.

---

### **5. Uses**

Multidimensional arrays are used in:

- mathematics (matrices, vectors),
- graphics (image pixels),
- machine learning (tensors),
- games and simulation (three-dimensional spaces).

---

**Summary:**

> **A multidimensional array** is an array whose elements are themselves arrays.
> It lets you store data as tables, matrices, or spatial grids and access elements using multiple indices.

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