Determinant nature

Upper triangular determinant

• N diagonal elements of the product on the spindle

　　

• Diagonal sub-sub-diagonal elements multiplied with the sign to be multiplied by (-1) ^{1/2 n-* (. 1-n-)} 

　　

 

• The ranks of the swap, the value of the determinant unchanged
• A row (column) have common factor k, k can be made
• The position of the transducer in two rows (columns), becomes determinant No.
• Two lines of the same, D = 0
• Two rows proportional, D = 0
• All the elements of a row are two numbers, the determinant can be written as the sum of two determinants, other elements in the same line of copy, write a number diverted to the previous two, after a write
• If the determinant of order n, each row is two and the number of win written 2 ⁿ n-order determinant and
• The value of k is a multiple of a row to another row, the same determinant

Tips

• Progressive sum
• By adding claw into a triangular column
• Claw determinant, edged, degree elevation

• Then add the line, simplifying determinant

Similar Vandermonde determinant

 

• Bordered method can be used

Eigenvalue

• Row addition, column addition
• Are there common factor observed, can be eliminated or proposed