A Note on the Lanczos Algorithm for Skew Symmetric Eigenvalue Problem

In[1]and[2]we disscussed the eigenvalue problem for real normal matrices and the eigenvalue problem for normal matrices in generalized inner product, respectively.In this note we will show that if matrix A is a skew symmetric. matrix (c.f.[1]) or matrix G is a B-skew symmetric matrix(c.f.[2]), then the Lanczos algorithm with respect to A or to G can be implemented by real arithmatic and is even simpler than that with respect to a symmetric matrix or to a B-symmetric matrix respectively.