def create_standard_basis(dimension, scale_factor=1.0):
    """Create an orthogonal, maximal, positive basis."""
    assert dimension >= 1
    assert scale_factor > 0.0
    pattern = []
    for i in range(dimension):
        for offset in (scale_factor, -scale_factor):
            vector = [0.0] * dimension
            vector[i] = offset
            pattern.append(vector)
    return pattern
