A repository that showcases my knowledge in Linear Algebra.
This is a conceptual demonstration, not production-ready code.
| Concept | Implementation Example |
|---|---|
| Vector Operations | Custom vector addition, subtraction, and scaling |
| Matrix Operations | Matrix multiplication, transposition, and inversion |
| Linear Transformations | Applying and composing linear transformations |
Key Notes:
LinPy is a Python package that demonstrates a deep understanding of linear algebra concepts through practical implementation. Unlike typical projects that rely on libraries like NumPy, LinPy is built using Python's built-in lists to perform vector and matrix operations, showcasing both theoretical knowledge and practical coding skills.
Limitations:
- only int|float components for Vector/Matrix instances are allowed.
- Vectors can only be 1D -> shape = (n,)
- Matrix can only be 2D -> shape = (n, m)
Clone the repository from GitHub:
git clone https://github.com/yourusername/LinPy.git
cd LinPyImport the package:
import linpy as lpCreate a few vectors and matrices:
import linpy as lp
# Create vectors
v1 = lp.Vector([1, 2, 3])
v2 = lp.Vector([4, 5, 6])
# Create matrices
m1 = lp.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
m2 = lp.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])Using Numpy arrays:
import numpy as np
# Create vectors from NumPy arrays
arr = np.array([1, 2, 3])
v3 = lp.Vector(arr)
# Create matrices from NumPy arrays
arr2 = np.array([[1, 2], [3, 4]])
m3 = lp.Matrix(arr2)print("v1 + v2 =", v1 + v2)
print("v1 - v2 =", v1 - v2)
print("v1 * 2 =", v1 * 2)
print("v1 . v2 =", v1 @ v2)
print("v1 x v2 =", v1.cross_product(v2))
print("Angle between v1 and v2 (degrees) =", v1.angle_between(v2))print("Magnitude of v1 =", v1.magnitude)
print("Length of v1 =", v1.length)
print("Shape of v1 =", v1.shape)
print("Number of dimensions of v1 =", v1.ndim)print("m1 + m2 =", m1 + m2)
print("m1 - m2 =", m1 - m2)
print("m1 * 2 =", m1 * 2)
print("m1 * v1 =", m1.apply_on_vector(v1))
print("m1 * m2 =", m1.apply_on_matrix(m2))
print("m1 composed with m2 =", m1.compose(m2))print("Transpose of m1 =", m1.transpose)
print("Diagonal of m1 =", m1.diagonal)
print("Anti-diagonal of m1 =", m1.anti_diagonal)
print("Trace of m1 =", m1.trace)
print("Anti-trace of m1 =", m1.anti_trace)
print("Is m1 symmetric? =", m1.is_symmetric)
print("Is m1 square? =", m1.is_square)
print("Is m1 diagonal? =", m1.is_diagonal)
print("Is m1 anti-diagonal? =", m1.is_anti_diagonal)
print("Is m1 an identity matrix? =", m1.is_identity)
print("Is m1 upper triangular? =", m1.is_upper_triangular)
print("Is m1 lower triangular? =", m1.is_lower_triangular)
print("Is m1 skew-symmetric? =", m1.is_skew_symmetric)
print("Rank of m1 =", m1.rank)
print("Is m1 full rank? =", m1.is_full_rank)
print("Determinant of m1 =", m1.determinant)
print("Inverse of m1 =", m1.inverse)
print("Is m1 singular? =", m1.is_singular)
print("Is m1 invertible? =", m1.is_invertable)
print("Is m1 a linear transformation? =", m1.is_linear_transformation)
print("Are columns of m1 linearly dependent? =", m1.is_linearly_dependent)
print("Span of m1 =", m1.span)
print("Do columns of m1 form a basis? =", m1.is_basis)
print("Is v1 a linear combination of columns of m1? =", m1.is_linear_combination(v1))| Function | Description | Parameters | Returns |
|---|---|---|---|
get_shape(data) |
Get the shape of the data | data: Iterable |
Tuple[int] |
zeros(shape) |
Create a zero matrix of given shape | shape: Tuple[int, int] |
List[List[int]] |
can_be_vector(data) |
Validate if data can be a vector | data: Iterable |
bool |
can_be_matrix(data) |
Validate if data can be a matrix | data: Iterable[Iterable] |
bool |
| Method | Description | Parameters | Returns |
|---|---|---|---|
__init__(data) |
Initialize a vector | data: List[Number] |
None |
angle_between(other, in_degrees) |
Calculate the angle between two vectors | other: Vector, in_degrees: bool |
float |
magnitude |
Calculate the magnitude of the vector | None | float |
length |
Get the length of the vector | None | int |
shape |
Get the shape of the vector | None | Tuple[int] |
ndim |
Get the number of dimensions of the vector | None | int |
cross_product(other) |
Calculate the cross product with another vector | other: Vector |
Vector |
cross_product(other) |
Calculate the cross product with another vector | other: Vector |
Vector |
| Property | Description |
|---|---|
magnitude |
Calculate the magnitude of the vector |
length |
Get the length of the vector |
shape |
Get the shape of the vector |
ndim |
Get the number of dimensions of the vector |
| Method | Description | Parameters | Returns |
|---|---|---|---|
__init__(data) |
Initialize a matrix | data: List[List[Number]] |
None |
apply_on_vector(vector) |
Apply the matrix as a linear transformation on a vector | vector: Vector |
Vector |
apply_on_matrix(matrix) |
Apply the matrix as a linear transformation on another matrix | matrix: Matrix |
Matrix |
compose(*matrices) |
Compose the current matrix with one or more matrices | *matrices: Matrix |
Matrix |
is_linear_combination(vector) |
Check if a vector is a linear combination of the columns of the matrix | vector: Vector |
bool |
| Property | Description |
|---|---|
rank |
Calculate the rank of the matrix using NumPy |
is_full_rank |
Check if the matrix is of full rank |
determinant |
Calculate the determinant of the matrix using NumPy |
inverse |
Calculate the inverse of the matrix using NumPy |
is_singular |
Check if the matrix is singular |
is_invertable |
Check if the matrix is invertible |
is_linear_transformation |
Check if the matrix represents a linear transformation |
is_linearly_dependent |
Check if the columns of the matrix are linearly dependent |
span |
Calculate the span of the matrix |
is_basis |
Check if the columns of the matrix form a basis |
transpose |
Get the transpose of the matrix |
T |
Get the transpose of the matrix (alias) |
diagonal |
Get the diagonal elements of the matrix |
anti_diagonal |
Get the anti-diagonal elements of the matrix |
trace |
Calculate the trace of the matrix |
anti_trace |
Calculate the anti-trace of the matrix |
is_symmetric |
Check if the matrix is symmetric |
is_square |
Check if the matrix is square |
is_diagonal |
Check if the matrix is diagonal |
is_anti_diagonal |
Check if the matrix is anti-diagonal |
is_identity |
Check if the matrix is an identity matrix |
is_upper_triangular |
Check if the matrix is upper triangular |
is_lower_triangular |
Check if the matrix is lower triangular |
is_skew_symmetric |
Check if the matrix is skew-symmetric |