# MatrixMania

This Package contains a few fundamental function which can be used for **matrices**.

## Functions:

- matmul function
- transpose function
- rot_2D function
- rot_3D function
- project_ortho

## matmul function:

This function calculates the matrix multiplication with 2 matrices. 
It also checks if the matrices are compatible for multiplication.

**Example:**

```
matrix_a =  [[3, 4, -1, 4],
             [-2, 2, 5, 1]]
             
matrix_b =  [[1, 3, -2],
             [2, 5, 1],
             [-1, 4, -4],
             [2, 3, 6]]
             
matrix_c = matmul(matrix_a, matrix_b)
print("matrix c:")
print(tabulate(matrix_c))
```

**Result:**

```
matrix c:
--  --  --
20  37  26
-1  27  -8
--  --  --
```


## transpose function:

This function transposes a matrix.

**Example:**

```
matrix = [[1, 2, 3],
          [4, 5, 6]]
          
new_matrix = transpose(matrix)
print("transposed matrix:")
print(tabulate(new_matrix))
```

**Result:**

```
transposed matrix:
-  -
1  4
2  5
3  6
-  -

```

## rot_2D function:

This function returns the rotation matrix for a given angle.

**Example:**

```
theta = math.pi / 2
R = rot_2D(theta)

print("rotation matrix for 90°:")
print(tabulate(R))
```

**Result**

```
rotation matrix for 90°:
-----------  ------------
6.12323e-17  -1
1             6.12323e-17
-----------  ------------
```

## rot_3D function:
This function calculates the rotation matrix for one 3D axis (x, y, z) for a certain angle.

**Example:**
```
theta = math.pi / 2
R = rot_3D(theta, "y")

print("rotation matrix for 90° on the y axis:")
print(tabulate(R))
```
**Result:**
```
rotation matrix for 90° on the y axis:
------------  -  -----------
 6.12323e-17  0  1
 0            1  0
-1            0  6.12323e-17
------------  -  -----------
```

## project_ortho function:
This functions projects a 3D point on a 2D display