Recently,　a　matrix-type　neural　dynamical　method　for　matrix-variable　nonlinear　optimization　with　box　constraints　was　presented.　This　paper　proposes　two　matrix-type　neural　dynamical　optimization　methods　for　matrix-variable　nonlinear　programming　with　linear　constraints.　Each　matrix-type　neural　dynamical　method　consists　of　continuous-time　and　discrete-time　models.　The　two　continuous-time　models　significantly　generalize　two　existing　vector-type　projection　neural　networks,　while　the　two　discrete-time　state　models　have　low　complexity　and　can　be　implemented　parallelly　by　matrix　operation.　Under　proper　conditions,　the　proposed　two　matrix-type　neural　dynamical　methods　are　guaranteed　to　converge　globally　to　the　optimal　solution.　Finally,　computed　examples　show　that　the　proposed　matrix-type　neural　dynamical　methods　for　matrix-variable　nonlinear　programming　with　linear　constraints　are　superior　to　current　matrix-type　neural　dynamical　methods　in　fast　computation.　©　2020　IEEE.