The maximum eigenvalue captures the signal correlation well, and the minimum eigenvalue also captures the noise characteristics well, thus the spectrum sensing algorithm based on the maximum and minimum eigenvalue gets better detection performance. This paper considers various combination algorithms based on maximum and minimum eigenvalues, and proposes some new spectrum sensing algorithms based on maximum and minimum eigenvalue which includes well known algorithm as its special case. Simulation result for multi-user, multi-antenna and multi-path scenarios shows the effectiveness of the proposed algorithms. In particular, the algorithm based on the product and sum of the maximum and minimum eigenvalues (α-MMEP and α-MMES) showed the best detection performance.