linalgkit-lab2 1.0.0

Linear-algebra toolkit: vector/matrix-space axioms, subspace checks, basis, norm, dimension, rank-nullity.

linalgkit-lab2

A clean, well-tested Python library for verifying fundamental linear-algebra properties — vector-space axioms, subspace conditions, basis extraction, norms, dimension, and the rank–nullity theorem.

---

Installation

pip install linalgkit-lab2

---

Quick Start

from linalgkit_lab2 import (
    check_vector_space,
    check_matrix_space,
    check_subspace,
    find_basis,
    find_norm,
    find_dimension,
    verify_rank_nullity,
    print_results,
)

# --- Vector space ---
result = check_vector_space([1, 2], [3, 4], a=2, b=3, zero_vector=[0, 0])
print_results("Vector Space", result)

# --- Matrix space ---
result = check_matrix_space([[1,2],[3,4]], [[5,6],[7,8]], a=2, b=3,
                             zero_matrix=[[0,0],[0,0]])
print_results("Matrix Space", result)

# --- Subspace ---
result = check_subspace([1, 2], [3, 4], a=2, b=3, zero_vector=[0, 0])
print_results("Subspace", result)

# --- Basis ---
basis = find_basis([[1,0,0],[0,1,0],[1,1,0]])
print("Basis:\n", basis)

# --- Norm ---
print("Norm:", find_norm([3, 4]))          # → 5.0

# --- Dimension ---
print("Dim:", find_dimension([[1,0],[0,1],[1,1]]))   # → 2

# --- Rank-nullity ---
print(verify_rank_nullity([[1,2,3],[4,5,6]]))

---

API Reference

check_vector_space(v1, v2, a, b, zero_vector) → dict

Returns a dict mapping each of the 10 standard vector-space axioms to True / False.

check_matrix_space(A, B, a, b, zero_matrix) → dict

Same as above but for 2-D matrices.

check_subspace(v1, v2, a, b, zero_vector) → dict

Checks the 3 subspace conditions plus an "Is Subspace" verdict key.

Key	What is checked
"Contains zero vector"	zero_vector is all-zeros and acts as additive identity
"Closed under addition"	v1 + v2 has correct shape, no NaN/Inf
"Closed under scalar multiplication"	a*v1, b*v2 have correct shape, no NaN/Inf
"Is Subspace"	All three above pass

find_basis(vectors) → ndarray

Greedy basis extraction. vectors is a 2-D array whose rows are vectors.

find_norm(vector) → float

Euclidean (L2) norm of a 1-D vector.

find_dimension(vectors) → int

Dimension of the span of the given row vectors (= matrix rank).

verify_rank_nullity(matrix) → dict

Returns {"rank", "nullity", "n_columns", "theorem_holds"}.

print_results(label, results)

Pretty-prints any result dict from the functions above.

---

Error Handling

All functions raise:

• TypeError — non-numeric inputs or non-real scalars
• ValueError — wrong dimensionality, empty inputs, shape mismatches, NaN/Inf values

---

License

MIT © manohar100323