The weighted logarithmic matrix norm and bounds of the matrix exponential Original Research Article

In this note the weighted logarithmic matrix norm is defined. The weighted logarithmic matrix norm is less than or equal to 2-logarithmic matrix norm. The bounds of the matrix exponential are obtained using the weighted logarithmic norm, which are sharper than those based on the 2-logarithmic matrix norm. Numerical examples are given to illustrate the results of the note.