Matrices Li Zhang Department of Mathematics Tongji University 4907 Tongji University】 1/14
. . Matrices Li Zhang Department of Mathematics Tongji University (Tongji University) Linear Algebra 1 / 14
Matrix Definition 7.0.1 a11 aml amn Note:m x n matrix,square matrix,entry,order,main diagonal,row matrix, column matrix The negative of a matrix is the matrix whose entries are the negatives of the original matrix. A zero matrix is one of any size all of whose entries are 0. Tongji University】 2/14
Matrix . Definition 7.0.1 . . a11 . . . a1n . . . . . . am1 . . . amn Note: m × n matrix, square matrix, entry, order, main diagonal, row matrix, column matrix The negative of a matrix is the matrix whose entries are the negatives of the original matrix. A zero matrix is one of any size all of whose entries are 0. (Tongji University) Linear Algebra 2 / 14
Matrix Definition 7.0.1 a11 aml amn Note:m x n matrix,square matrix,entry,order,main diagonal,row matrix, column matrix The negative of a matrix is the matrix whose entries are the negatives of the original matrix. A zero matrix is one of any size all of whose entries are 0. Tongji University】 2/14
Matrix . Definition 7.0.1 . . a11 . . . a1n . . . . . . am1 . . . amn Note: m × n matrix, square matrix, entry, order, main diagonal, row matrix, column matrix The negative of a matrix is the matrix whose entries are the negatives of the original matrix. A zero matrix is one of any size all of whose entries are 0. (Tongji University) Linear Algebra 2 / 14
Matrix addition Definition 7.1.1 (Matrix addition) a11...a1n b11..b1n a11+b11.a1n+b1n 十 .. = am1...amn bm1...bmn aml bmi...amn bmn 04十B=B十 ©H+B)+C=过+(B+C 0A+B一C=4-C+B 04十B=C+D=4+B-C=D Tongji University】 3/14
Matrix addition . Definition 7.1.1 (Matrix addition) . . a11 . . . a1n . . . . . . am1 . . . amn + b11 . . . b1n . . . . . . bm1 . . . bmn := a11 + b11 . . . a1n + b1n . . . . . . am1 + bm1 . . . amn + bmn .1 A + B = B + A. .2 (A + B) + C = A + (B + C) 3. A + B − C = A − C + B .4 A + B = C + D ⇒ A + B − C = D (Tongji University) Linear Algebra 3 / 14
Matrix addition Definition 7.1.1 (Matrix addition) a11...a1n b11..b1n a11+b11.a1n+b1n 十 三 am1...amn bm1...bmn aml十bml..amm+bmm OA+B=B+A. ⊙(A+B)+C=A+(B+C) A+B-C=A-C+B OA+B=C+D→A+B-C=D Tongji University】 3/14
Matrix addition . Definition 7.1.1 (Matrix addition) . . a11 . . . a1n . . . . . . am1 . . . amn + b11 . . . b1n . . . . . . bm1 . . . bmn := a11 + b11 . . . a1n + b1n . . . . . . am1 + bm1 . . . amn + bmn .1 A + B = B + A. .2 (A + B) + C = A + (B + C) 3. A + B − C = A − C + B .4 A + B = C + D ⇒ A + B − C = D (Tongji University) Linear Algebra 3 / 14