线性代数
transpose
Matrix transpose()
获取矩阵对应的转置矩阵
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1]
]);
mt.transpose().visible();
}
output
[
[ 1 3 9]
[ 4 -2 0]
[ 5 1 1]
]
trace
double trace()
获取矩阵最小维度下主对角线上数据的和，方阵中的迹
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
print(mt.trace());
}
output
0.0
bool get isSquare
判断矩阵是不是方阵，即row == column
coincidental
Matrix coincidental({required int row, required int column})
获取余子式，即去掉某行和某列而拼成的矩阵
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
mt.coincidental(row: 0, column: 1).visible();
}
output
[
[ 3 1]
[ 9 1]
[ 5 2]
]
elementary_exchange
void elementary_exchange({required int index1, required int index2, bool horizontal = true})
初等变换——交换行或者列
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
mt
..elementary_exchange(index1: 3, index2: 2, horizontal: true)
..visible()
..elementary_exchange(index1: 0, index2: 1, horizontal: false)
..visible();
}
output
[
[ 1 4 5]
[ 3 -2 1]
[ 5 3 2]
[ 9 0 1]
]
[
[ 4 1 5]
[ -2 3 1]
[ 3 5 2]
[ 0 9 1]
]
elementary_multiply
void elementary_multiply({required int index, required double number, bool horizontal = true})
初等变换——倍乘行或者列
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.2f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
mt
..elementary_multiply(index: 1, number: 2.0, horizontal: false)..visible()
..elementary_multiply(index: 1, number: 0.5, horizontal: true)..visible();
}
output
[
[ 1.00 8.00 5.00]
[ 3.00 -4.00 1.00]
[ 9.00 0.00 1.00]
[ 5.00 6.00 2.00]
]
[
[ 1.00 8.00 5.00]
[ 1.50 -2.00 0.50]
[ 9.00 0.00 1.00]
[ 5.00 6.00 2.00]
]
elementary_add
void elementary_add({required int index1, required int index2, required double number, bool horizontal = true})
初等变换——把某行或者列的倍乘加到另一行或者列
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.2f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
mt
..elementary_add(index1: 1, index2: 2, number: 1, horizontal: true)
..visible()
..elementary_add(index1: 2, index2: 1, number: 3, horizontal: false)
..visible();
}
output
[
[ 1.00 4.00 5.00]
[12.00 -2.00 2.00]
[ 9.00 0.00 1.00]
[ 5.00 3.00 2.00]
]
[
[ 1.00 4.00 17.00]
[12.00 -2.00 -4.00]
[ 9.00 0.00 1.00]
[ 5.00 3.00 11.00]
]
dot
Matrix dot({required Matrix other})
左行右列做矩阵内积，必须满足$A_(mn)$和$B_(nk)$的形状
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.2f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
var mt1 = Matrix.fromList(
[[1, 4, 5],
[3, -2, 1],
[9, 0, 1],]
);
mt.dot(other: mt1).visible();
}
output
[
[58.00 -4.00 14.00]
[ 6.00 16.00 14.00]
[18.00 36.00 46.00]
[32.00 14.00 30.00]
]
kronecker
Matrix kronecker({required Matrix other})
关于克罗内克积
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%3.2f";
var mt = Matrix.fromList([
[1, 4, 5],
[3, -2, 1],
[9, 0, 1],
[5, 3, 2]
]);
var mt1 = Matrix.fromList(
[[1, 4, 5],
[3, -2, 1],
[9, 0, 1],]
);
mt.kronecker(other: mt1).visible();
}
output
[
[ 1.00 4.00 5.00 4.00 16.00 20.00 5.00 20.00 25.00]
[ 3.00 -2.00 1.00 12.00 -8.00 4.00 15.00 -10.00 5.00]
[ 9.00 0.00 1.00 36.00 0.00 4.00 45.00 0.00 5.00]
[ 3.00 12.00 15.00 -2.00 -8.00 -10.00 1.00 4.00 5.00]
[ 9.00 -6.00 3.00 -6.00 4.00 -2.00 3.00 -2.00 1.00]
[ 27.00 0.00 3.00 -18.00 -0.00 -2.00 9.00 0.00 1.00]
[ 9.00 36.00 45.00 0.00 0.00 0.00 1.00 4.00 5.00]
[ 27.00 -18.00 9.00 0.00 -0.00 0.00 3.00 -2.00 1.00]
[ 81.00 0.00 9.00 0.00 0.00 0.00 9.00 0.00 1.00]
[ 5.00 20.00 25.00 3.00 12.00 15.00 2.00 8.00 10.00]
[ 15.00 -10.00 5.00 9.00 -6.00 3.00 6.00 -4.00 2.00]
[ 45.00 0.00 5.00 27.00 0.00 3.00 18.00 0.00 2.00]
]
double get det
求方阵的行列式值，基于高斯消元法
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%3.2f";
var mt = Matrix.fromList([
[1, 4, 5, 5],
[3, -2, 1, 3],
[9, 0, 1, 2],
[5, 3, 2, -5]
]);
print(mt.det);
}
output
-708.0
Matrix get adjugate
获取方阵的伴随矩阵
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%5.2f";
var mt = Matrix.fromList([
[1, 4, 5, 5],
[3, -2, 1, 3],
[9, 0, 1, 2],
[5, 3, 2, -5]
]);
print(mt.adjugate);
}
output
[
[ 15.00 21.00 -84.00 -6.00]
[ -67.00 331.00 -144.00 74.00]
[ -47.00 -349.00 216.00 -170.00]
[ -44.00 80.00 -84.00 112.00]
]
Matrix get inverse
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%5.2f";
var mt = Matrix.fromList([
[1, 4, 5, 5],
[3, -2, 1, 3],
[9, 0, 1, 2],
[5, 3, 2, -5]
]);
print(mt.inverse);
}
output
[
[ -0.02 -0.03 0.12 0.01]
[ 0.09 -0.47 0.20 -0.10]
[ 0.07 0.49 -0.31 0.24]
[ 0.06 -0.11 0.12 -0.16]
]
Matrix get rref
获取矩阵对应的行最简形矩阵
int get rank
矩阵的秩
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%5.2f";
var mt = Matrix.fromList([
[1, 4, 5, 5],
[3, -2, 1, 3],
[9, 0, 1, 2],
[5, 3, 2, -5]
]);
print(mt.rank);
mt[3] = [1 - 9, 4 - 0, 5 - 1, 5 - 2]; // row_index0 - row_index2
print(mt.det);
print(mt.rank);
}
output
4
0.0
3