A matrix with a row of zeros has det A = 0. If A is triangular then detA=a11a22...anndetA=a11a22...ann=product of diagnonal entries. If A is singular then det A = 0. If A is invertible then detA≠0detA≠0. The determinant of AB is det A times det B : |AB|=|A||B||...
This step does not change the determinant (Property 3), so the determinant of the original matrix is equal to the determinant of a matrix with a row of zeros, which is zero (Property 4). But in this case at least one of the diagonal entries of the upper triangular matrix is 0, so ...
Every suchdeterminantis zero, because one row can be made all zeros by adding to it all of the other rows 每个这种行列式都为零,因其中一行加上全体其它行时,能使该行变成全为零。 属类:综合句库-- Peasants are theDeterminantfactors of New Rural Construction ...
</m> We also recover the fact that a matrix with a row or column of zeros has determinant zero. </p> <example> <p> The following matrices all have zero determinant: <me> \mat{0 2 -1; 0 5 10; 0 -7 3},\quad \mat{5 -15 11; 3 -9 2; 2 -6 16},\quad \...
Minor rank, zeros of the determinant of a Boolean matrix, and their applicationsdoi:10.1515/dma.2011.037V. B. PoplavskiiDiscrete Mathematics and Applications
DefinitionofthedeterminantofamatrixWitheachsquarematrix,itispossibletoassociatearealnumbercalledthedeterminantofthematrix.Introduction–importa..
is a 2 × 3 matrix. A matrix withnrows andncolumns is called asquare matrix of ordern. An ordinary number can be regarded as a 1 × 1matrix; thus, 3 can be thought of as the matrix [3]. A matrix with only one row andncolumns is called a rowvector, and a matrix with only ...
The determinant of a matrix is equal to that of its transpose. In essence, if instead of the matrix we started with, we "flip it" so that its first row will be the first column, the first column will be the first row, etc. (this is called the transposition of a matrix), then th...
Consider a matrix of order n, that is, a square array of n2 elements, for example, numbers or functions: Each element of the matrix is specified by two indices. The element aij belongs to the i th row and the j th column. The determinant of the matrix (1) is a polynomial in the...
If D is the determinant of a square matrix A of order n, then the determinant of its adjoint is