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[linear algebra] 1.1 second and third order determinants

2022-06-29 02:43:00 【Michael_ Lzy】

One 、 Second order determinant

Binary linear equations :

hold $a_{11} a_{22} a_{12} a_{21}$ These four numbers are listed in the equations (1) Position in , A table of numbers arranged in two rows and two columns

expression $a_{11}a_{22}-a_{12}a_{21}$ Called a digital meter (3) Identified Second order determinant , And write it down

Count $a_{ij}$ (i=1,2;j=1,2) It's called a determinant (4) Of Elements or element .

Elements $a_{ij}$ The first subscript of i be called Line mark , Indicates that the element is in the i That's ok ; The second subscript j be called Column mark , Indicates that the element is in the j Column .

Located at i Xing di j The elements of a column are called determinants (4) Of (i,j) element .

The definition of the above second-order determinant , Diagonal rule can be used to remember .

See picture 1.1, hold a11 To a22 The real line of is called The main diagonal ,a12 To a21 The virtual line of is called Sub diagonal .

The second-order determinant is The product of two elements on the main diagonal subtract The product of two elements on the sub diagonal The difference obtained .