Problems

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Calculate Eigenvalues of a Matrix

Linear Algebra

Medium

Calculate the eigenvalues of a square matrix.

Eigenvalue Definition:

Av = \lambda v

Characteristic Equation:

\det(A - \lambda I) = 0

Where: A = matrix, λ = eigenvalue, v = eigenvector, I = identity matrix, det = determinant

Function Arguments

matrix: list[list[float]] | np.ndarray - Input matrix (should be square)

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Examples

Input: matrix=[[4, 1], [2, 3]]

Output: [2.0, 5.0] (approximately)

Input: matrix=[[0, -1], [1, 0]]

Output: [-1j, 1j] (pure imaginary)

Input: matrix=[[1, 2, 3], [4, 5]]

Output: None (non-square)

Hint 1

Use np.asarray() to convert input to numpy array. Check matrix dimensions with .shape and .ndim.

Hint 2

Use np.linalg.eigvals() to compute eigenvalues. Use np.lexsort() for consistent sorting by real then imaginary parts.

Hint 3

Handle edge cases: check if matrix is square with matrix.shape[0] == matrix.shape[1]. Return None for invalid inputs.

Requirements

Return np.ndarray of eigenvalues (complex dtype if needed)
Return None for non-square matrices or invalid input
Handle empty matrices gracefully
Sort eigenvalues by real part, then imaginary part for consistency
Use NumPy's linear algebra functions

Constraints

Matrix size ≤ 100×100
Numerical precision: relative tolerance ≤ 1e-8
Libraries: NumPy only

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