TheAlgorithms/Python · error · ValueError

Invalid matrix dimensions

Error message

Invalid matrix dimensions

What it means

Raised by matrix_multiply_recursive when either input matrix is not square, or the two matrices do not have the same dimension. This recursive block-multiplication implementation only supports equal-sized square matrices (it splits matrices into quadrants), which is far stricter than general matrix multiplication. Empty matrices short-circuit to [] instead.

Source

Thrown at matrix/matrix_multiplication_recursion.py:113

    >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_wide)
    Traceback (most recent call last):
        ...
    ValueError: Invalid matrix dimensions
    >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_high)
    Traceback (most recent call last):
        ...
    ValueError: Invalid matrix dimensions
    >>> matrix_multiply_recursive(matrix_1_to_4, matrix_count_up)
    Traceback (most recent call last):
        ...
    ValueError: Invalid matrix dimensions
    """
    if not matrix_a or not matrix_b:
        return []
    if not all(
        (len(matrix_a) == len(matrix_b), is_square(matrix_a), is_square(matrix_b))
    ):
        raise ValueError("Invalid matrix dimensions")

    # Initialize the result matrix with zeros
    result = [[0] * len(matrix_b[0]) for _ in range(len(matrix_a))]

    # Recursive multiplication of matrices
    def multiply(
        i_loop: int,
        j_loop: int,
        k_loop: int,
        matrix_a: Matrix,
        matrix_b: Matrix,
        result: Matrix,
    ) -> None:
        """
        :param matrix_a: A square Matrix.
        :param matrix_b: Another square Matrix with the same dimensions as matrix_a.
        :param result: Result matrix
        :param i: Index used for iteration during multiplication.

View on GitHub (pinned to f5988cc097)

Solutions

1. Pre-check with the module's is_square() helper on both matrices and len equality before calling.
2. If your matrices are rectangular but compatible (cols_a == rows_b), use the general algorithm in matrix_operation.multiply or matrix_class.Matrix.__mul__ instead.
3. Pad rectangular matrices to square with zero rows/columns if the algorithm's constraint is acceptable for your use case, then trim the result.
4. Rename expectations in tests: this function's contract is same-size square matrices only.

Example fix

# before
result = matrix_multiply_recursive(a_2x3, b_3x3)  # ValueError

# after
from matrix.matrix_operation import multiply
result = multiply(a_2x3, b_3x3)  # general multiplication

from matrix.matrix_multiplication_recursion import is_square

if not matrix_a or not matrix_b:
    result = []
elif len(matrix_a) != len(matrix_b) or not is_square(matrix_a) or not is_square(matrix_b):
    raise ValueError("recursive multiply requires two equal-size square matrices")
else:
    result = matrix_multiply_recursive(matrix_a, matrix_b)

def is_uniform_square_pair(a: list, b: list) -> bool:
    """Guard: both non-empty square nested lists of the same dimension."""
    return (
        bool(a) and bool(b)
        and isinstance(a, list) and isinstance(b, list)
        and len(a) == len(b)
        and all(len(r) == len(a) for r in a)
        and all(len(r) == len(b) for r in b)
    )

try:
    result = matrix_multiply_recursive(a, b)
except ValueError as e:
    if "Invalid matrix dimensions" in str(e):
        from matrix.matrix_operation import multiply
        result = multiply(a, b)  # general algorithm handles compatible rectangles
    else:
        raise

When it happens

Trigger: matrix_multiply_recursive([[1, 2], [3, 4]], [[1, 2, 3], [4, 5, 6]]) (second not square), or multiplying a 2x2 by a 3x3. Any non-square operand or size mismatch between two square operands triggers it.

Common situations: Assuming this helper is a general multiplier because of its name; feeding rectangular data matrices from a dataset; porting code from NumPy dot() which handles any compatible shapes.

Related errors

• Only square matrices can be raised to a power
• Matrix is not square
• double_factorial_recursive() only accepts integral values
• double_factorial_recursive() not defined for negative values
• power is negative

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/f0fa6bb0a91c9828. Report an issue: GitHub.