Determinant can be regarded as a generalization of the concept of directed area or volume in general Euclidean space. In other words, in N-dimensional Euclidean space, determinant describes the influence of a linear transformation on "volume".
Chinese name
decisive factor
Foreign name
Determinant (English) Determinant (French)
express
D=|A|=detA=det(aij)
Applied discipline
linear algebra
area of application
Mathematics, physics
quick
navigate by water/air
nature
mathematic definition
N-order determinant
set up
It is an N-order square array with n2 numbers aij(i, j= 1, 2, ..., n), and its value is n! Sum of terms
Where k 1, k2, ..., kn are exchanged by the sequence 1, 2, ..., n represents k times, and σ represents k 1, k2, ..., kn. The form is as follows
The sum of the items of, where a 13a2 1a34a42 corresponds to k=3, that is, the symbol before the item should be
(- 1)3.
If the n-order square matrix A=(aij), then the determinant D corresponding to A is recorded as
D=|A|=detA=det(aij)
If the determinant d of matrix A is equal to 0, it is called singular matrix, otherwise it is called nonsingular matrix.
Tag set: any k elements I 1, I 2, ..., n are satisfied in the sequence i 1, i2, ..., ik.
1≤I 1 & lt； i2 & lt...& ltik≤n( 1)
I 1, i2, ..., ik has k {1, 2, ..., n} and {1, 2, ..., n} denoted as C.
Subcolumn. Therefore, C(n, k) is a labeled set with elements (see Chapter 2 1, 2), and the elements of C(n, k) are σ, τ, ..., σ∈C(n, k).
σ={i 1，i2，...，ik}
It's {1, 2, ..., n}. If τ={j 1, j2, ..., jk}∈C(n, k), then σ = τ means i65438.