週期矩陣常常出現在動態系統的學習上,而保秩的矩陣在微分代數系統也是很重要地.在本篇論文中我們考慮以下平滑及週期的線性矩陣方程其係數為保秩的線性矩陣係數. (1.1) A(t)x(t)=b(t), (1.2) A(t)X(t)B(t)=E(t), (1.3) A(t)X(t) + Y(t)B(t)=C(t), (1.4) A(t)X(t)B(t) + C(t)Y(t)D(t)=E(t). 因為它們可能無解所以我們有興趣的是以下平滑及週期的最小l_2-解的問題. (1.1a) min||A(t)x(t)-b(t)||_2 (1.2a) min||A(t)X(t)B(t)-E(t)||_2 (1.3a) min||A(t)X(t)+Y(t)B(t)-C(t)||_2 (1.4a) min||A(t)X(t)B(t)+C(t)Y(t)D(t)-E(t)||_2 Periodic matrices arise quite often in the study of dynamics. The matrices with constant rank is important in applications related to differential algebraic system.In this paper we consider the following smooth and periodic linear matrix equations with constant rank matrix coefficients respectively. (1.1) A(t)x(t)=b(t), (1.2) A(t)X(t)B(t)=E(t), (1.3) A(t)X(t) + Y(t)B(t)=C(t), (1.4) A(t)X(t)B(t) + C(t)Y(t)D(t)=E(t). Because they may be inconsistent (i.e., have no solution), we are interesting in the following smooth and periodic minimal l_2-solution problems respectively. (1.1a) min||A(t)x(t)-b(t)||_2 (1.2a) min||A(t)X(t)B(t)-E(t)||_2 (1.3a) min||A(t)X(t)+Y(t)B(t)-C(t)||_2 (1.4a) min||A(t)X(t)B(t)+C(t)Y(t)D(t)-E(t)||_2
