Is it Islamically permissible for a woman whose husband has passed away to prepare a feast after her iddah (waiting period) has ended and invite people to it, in order to show that she has completed her iddah?

There is no objection to a woman hosting a feast (walimah) to celebrate the end of her waiting period (iddah), as it falls under what is done for joyous occasions, such as the return of a traveler or the circumcision of a newborn. The basic principle is that it is permissible. The one who performs it will be rewarded if she intends to thank Allah Almighty, feed her brethren, and bring joy to them. This feast is not performed as an act of worship, nor is it customary every year, so it does not fall under innovation (bidah) or imitation of the disbelievers. Scholars have mentioned that feasts are of three types: those that are forbidden, such as mourning feasts (ma'tam); those that are legally prescribed, such as the wedding feast (walimat an-nikah); and those that are permissible, such as a feast for a woman exiting postpartum bleeding (nifas), or for circumcision, or for moving into a new home.