Determinants. Designed for High Schools And the Lower Classes of Colleges And Universities
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11. A determinant of « rows and n columns is called a determinant of the nth order, n being any positive whole number.
12. The convention for such an expression is that it rep- resents the algebraic sum of all the products formed by taking one and only one element from each row and one and only one element from each column.
13. The elements of any constituent are so written that the symbols representing the elements shall stand in the order of the columns from which they are taken. The numbers ...indicating the rows from which they are taken are written in a horizontal line.
14. The Sign Symbol, of the constituent is (— 1) ", w being the number of inversions of order in the line.
To explain what is meant by an inversion we will take the determinant '\ c.
I2 0^ Cl^ O2 I ^3 ^2 «! - C3 «2 '^1- In the first three constituents of this development, the subscripts are in their natural order; hence, there are no inversions- In the last three constituents the subscripts may be ar- ranged in a line as follows: 3 2 1 Here 3 stands before 2 and 1, and 2 stands before 1; hence, there are three inversions.
What to read after Determinants. Designed for High Schools And the Lower Classes of Colleges And Universities?
You can find similar books in the "Read Also" column, or choose other free books by James M James Morford Taylor to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
11. A determinant of « rows and n columns is called a determinant of the nth order, n being any positive whole number.
12. The convention for such an expression is that it rep- resents the algebraic sum of all the products formed by taking one and only one element from each row and one and only one element from each column.
13. The elements of any constituent are so written that the symbols representing the elements shall stand in the order of the columns from which they are taken. The numbers ...indicating the rows from which they are taken are written in a horizontal line.
14. The Sign Symbol, of the constituent is (— 1) ", w being the number of inversions of order in the line.
To explain what is meant by an inversion we will take the determinant '\ c.
I2 0^ Cl^ O2 I ^3 ^2 «! - C3 «2 '^1- In the first three constituents of this development, the subscripts are in their natural order; hence, there are no inversions- In the last three constituents the subscripts may be ar- ranged in a line as follows: 3 2 1 Here 3 stands before 2 and 1, and 2 stands before 1; hence, there are three inversions.
What to read after Determinants. Designed for High Schools And the Lower Classes of Colleges And Universities?
You can find similar books in the "Read Also" column, or choose other free books by James M James Morford Taylor to read onlineMoreLess
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