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MATRICES Numerical Methods Applied to Mechatronics Dr. Jorge A. Olórtegui Yume, Ph.D. Mechatronics Engineering School National University of Trujillo Matrices Dr. Jorge A. Olortegui Yume, Ph.D. 2 OVERVIEW ã MATRIX : Rectangular array of elements represented by a single symbol (Ex.: [A]). ã ELEMENT: Individual entry of a matrix (Ex.: a 23 ) Matrices Dr. Jorge A. Olortegui Yume, Ph.D. 3 OVERVIEW (cont´d) ã Row: A horizontal set of elements ã Column: Vertical set of elements. ã The first subscrip
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  MATRICES Numerical Methods Applied to MechatronicsDr. Jorge A. OlórteguiYume, Ph.D. MechatronicsEngineeringSchoolNationalUniversityof Trujillo  Matrices Dr. Jorge A. OlorteguiYume Ph.D. 2 OVERVIEW ã MATRIX : Rectangulararray of elements represented by a single symbol (Ex.: [  A ]). ã ELEMENT: Individualentry of a matrix(Ex.: a 23 )  Matrices Dr. Jorge A. OlorteguiYume Ph.D. 3 OVERVIEW (cont´d) ã Row: A horizontal set of elements ã Column: Verticalset of elements. ã The first subscript of an element indicates the row while the second indicates the column. ã Matrix Size: m by n (or m x n ). ã 1 x n matrices are row vectors . ã  m x 1 matrices are column vectors. (Ex.: a 23 )   131211  aaa  312111 aaa  Matrices Dr. Jorge A. OlorteguiYume Ph.D. 4 SPECIAL MATRICES ã Matrices where m = n are called square matrices . ã There are a number of special forms of square matrices: Symmetric  A    5 1 21 3 72 7 8           Diagonal  A    a 11 a 22 a 33           Identity  A    111           Upper Triangular   A    a 11  a 12  a 13 a 22  a 23 a 33           Lower Triangular   A    a 11 a 21  a 22 a 31  a 32  a 33           Banded  A    a 11  a 12 a 21  a 22  a 23 a 32  a 33  a 34 a 43  a 44            

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