A series 16+8+4+2+1 is replaced by the series 16+8+4+2, then it is called
Each number in the sequence is half the value of the number receding it. So the common difference in the series is dividing by two.
The answer is ½ or 0.5
When you keep dividing by two, you will notice an interesting pattern: the denominator continues to increase by two, while the numerator value remains the same. That’s fascinating because in natural, whole numbers the numbers in the series would decrease by two.
If n x n matrices A and B are similar, then they have the same eigenvalues (with the same multiplicities).
Since similar matrices A and B have the same characteristic polynomial, they also have the same eigenvalues. If B = PAP−1 and v = 0 is an eigenvector of A (say Av = λv) then B(Pv) = PAP−1(Pv) = PA(P−1P)v = PAv = λPv. Thus Pv (which is non-zero since P is invertible) is an eigenvector for B with eigenvalue λ.