character analysis of Kate Petruchio, Bianca and Lucentio

Kate, is indeed fitting of all descriptions from the locals at the beginning of the play, and seems to be driven to act as those descriptions say out of anger at those who proffer those descriptions and in part out of her father's favoritism for Bianca.  However, when she encounters someone who appears to truly love her, she slowly transforms into a woman of good nature.   Petruchio starts his role in the play as trying to obtain Kate's hand in marriage in main part for her large dowry, and in minor part to have a bit of fun in bemusing Kate and everyone else with his antics of wooing her.  However he soon truly falls in love with his wife and begins to attempt to "tame" her out of true affection, instead of for his own entertainment.  Bianca appears to be a character much like Hero from Much ado about nothing, saying little of any substance and serving as mere contrast to Kate.  Lucentio again parallels Claudio from much ado, seeing Bianca, falling in love immediately and running into some difficulty in obtaining her and in marriage.