J. Sylvester, Sur l’equations en matrices , C.R. Acad. Sci. Paris, 99 (1884), pp. 67 – 71, pp. 115 – 116.
R. H. Bartels and G. W. Stewart, Solution of the matrix equation , Comm. ACM, 15 (1972), pp. 820 – 826.
R. Bhatia and P. Rosenthal, How and why to solve the operator equation ?, Bull. London Math. Soc., 29 (1997), pp. 1 – 21.
S.-G. Lee and Q.-P. Vu, Simultaneous solutions of Sylvester equations and idempotent matrices separating the joint spectrum, Linear Algebra and its Applications, 435 (2011), pp. 2097 – 2109.
แหล่งข้อมูลอื่น
Online solver for arbitrary sized matrices.[ลิงก์เสีย]
มีนาคม 07, 2022
สมการซ, ลเวสเตอร, งก, ามภาษา, ในบทความน, ไว, ให, านและผ, วมแก, ไขบทความศ, กษาเพ, มเต, มโดยสะดวก, เน, องจากว, เด, ยภาษาไทยย, งไม, บทความด, งกล, าว, กระน, ควรร, บสร, างเป, นบทความโดยเร, วท, งกฤษ, sylvester, equation, กพบในทฤษฎ, ระบบควบค, อสมการเมทร, กซ, ในร, ปแบ. lingkkhamphasa inbthkhwamni miiwihphuxanaelaphurwmaekikhbthkhwamsuksaephimetimodysadwk enuxngcakwikiphiediyphasaithyyngimmibthkhwamdngklaw krann khwrribsrangepnbthkhwamodyerwthisudsmkarsilewsetxr xngkvs Sylvester equation mkphbinthvsdirabbkhwbkhum khuxsmkaremthriks inrupaebb A X X B C displaystyle AX XB C odythi A B X C displaystyle A B X C khux n n displaystyle n times n emthriks A B C displaystyle A B C epnemthriksthrabkha aela X displaystyle X khuxemthrikstwaeprthieratxngkarhakha enuxha 1 enguxnikhkarmixyuaelakhwamepnidxyangediywkhxngphltxb 2 khatxbechingelkh 3 duephim 4 xangxing 5 aehlngkhxmulxunenguxnikhkarmixyuaelakhwamepnidxyangediywkhxngphltxb aekikhodyich phlkhunokhnenkekxr Kronecker product aelatwdaeninkarthithakareriyngsxnkhxlmn vectorization operator vec displaystyle operatorname vec erasamarthekhiynsmkarinrupaebbihmidepn I n A B T I n vec X vec C displaystyle I n otimes A B T otimes I n operatorname vec X operatorname vec C odythi I n displaystyle I n khux n n displaystyle n times n emthriksexklksn inrupaebbnieracaehnidwa smkarsilewsetxr samarthekhiynidxyuinrup rabbechingesn thimimitikhnad n 2 n 2 displaystyle n 2 times n 2 hmayehtu xyangirkdikarekhiynsmkarsilewsetxr inrupaebbniimepnthiaenanakbkarichinkarhaphltxbechingelkh numerical solution ephraaepnkarichkhntxnkarkhanwnthimakekinipaelacathaihekidkhxphidphladidtha A U L U 1 displaystyle A ULU 1 aela B T V M V 1 displaystyle B T VMV 1 xyuinrupaebbbyyticxraedn Jordan canonical form khxng A displaystyle A aela B T displaystyle B T aelw aela l i displaystyle lambda i aela m j displaystyle mu j khuxkhalksnaechphaa eigenvalue khxng A displaystyle A aela B T displaystyle B T tamladb aelw erasamarthekhiynsmkarinrup I n A B T I n V U I n L M I n V U 1 displaystyle I n otimes A B T otimes I n V otimes U I n otimes L M otimes I n V otimes U 1 enuxngcak I n L M I n displaystyle I n otimes L M otimes I n khux emthrikssamehliymbn upper triangular thimismachiktamaenwthaeyngepn l i m j displaystyle lambda i mu j emthriksdansaymuxcaepnemthriksexkthan singular ktxemux mi i displaystyle i aela j displaystyle j thithaih l i m j displaystyle lambda i mu j dngnn erasamarthphisucnwasmkarsilewsetxrmikhatxbthiimsa unique solution ktxemux A displaystyle A aela B displaystyle B immikhalksnaechphaathirwmknkhatxbechingelkh aekikhkhntxnwithikhxng barethl aela chwars Bartels Stewart algorithm samarthhakhatxbkhxngsmkarsilewsetxr odykarepliyn A displaystyle A aela B displaystyle B ihxyuinrupkhxngaebbkhxngchur Schur form odyich khntxnwithikhiwxar QR algorithm aelatxmaaeksmkarthitidinrupemthrikssamehliymbndwy back substitution khntxnwithidngklawmikha O n 3 displaystyle n 3 duephim aekikhsmkareliypunxf smkarrikkatiechingphuchkhnit Algebraic Riccati equation xangxing aekikhJ Sylvester Sur l equations en matrices p x x q displaystyle px xq C R Acad Sci Paris 99 1884 pp 67 71 pp 115 116 R H Bartels and G W Stewart Solution of the matrix equation A X X B C displaystyle AX XB C Comm ACM 15 1972 pp 820 826 R Bhatia and P Rosenthal How and why to solve the operator equation A X X B Y displaystyle AX XB Y Bull London Math Soc 29 1997 pp 1 21 S G Lee and Q P Vu Simultaneous solutions of Sylvester equations and idempotent matrices separating the joint spectrum Linear Algebra and its Applications 435 2011 pp 2097 2109 aehlngkhxmulxun aekikhOnline solver for arbitrary sized matrices lingkesiy ekhathungcak https th wikipedia org w index php title smkarsilewsetxr amp oldid 9668083, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,