Tổng hợp kiến thức Toán Cao Cấp (AAAclass) – TOÁN CAO CẤP CHƯƠNG I. MÔ HÌNH TUYẾN TÍNH và ĐẠI SỐ MA – Studocu
1
TOÁN CAO CẤP
CHƯƠNG I. MÔ HÌNH TUYẾN TÍNH và ĐẠI SỐ MA
TRẬN
I.1. MA TRẬN
1.
KHÁI NIỆM
a)
Ma trận cấp
m
n
: là một bảng
gồm
m
n
số
ij
a
được sắp xếp thàn
h
m
dòng
và
n
cột dưới dạng
11
12
1
21
22
2
1
2
…
…
…
…
…
…
…
n
n
m
m
mn
a
a
a
a
a
a
A
a
a
a
ij
a
là phần tử ở dòng
i
và cột
j
của ma trận
A
;
i
là chỉ số dòng,
j
là chỉ số cột
của phần tử
ij
a
đó.
Ví dụ 1.
1
2
3
456
A
là m
a trận cấp
2
3
, trong ma trận này
ta có phần tử
13
21
3
,
4
a
a
.
Người ta thường
viết tắt ma trận ở
dạng
ij
m
n
A
a
.
b)
Ma trận vuông
:
là ma trận có số d
òng
m
bằng số cột
n
, khi đó thay vì nói m
a
trận cấp
n
n
ta chỉ nói đó
là ma trận vuông cấp
n
.
Ví dụ 2.
1
3
5
7
B
là ma trận vuông cấp ha
i.
Trong m
a trận vuông cấp
n
, người ta gọi các
phần tử
11
22
,
,
…,
nn
a
a
a
là các phần
tử thuộc đường c
héo chính của m
a trận.
c)
Ma trận đơn vị
: là ma trận vuông có tấ
t cả các phần tử t
huộc đường ch
éo chính
đều bằng 1, các phần
tử còn lại đều
bằng 0,kí hiệu
là
n
I
.
Ví dụ 3.
2
3
1
0
0
1
0
,
0
1
0
0
1
0
0
1
I
I
là các m
a trận
đơn vị cấp
2, cấp 3
d)
Ma trận tam giác:
l
à m
a trận vuông có tất cả các phầ
n tử nằm
phía dưới, hoặc
phía
trên đường chéo c
hính đều bằng
0.
Ví dụ 4.
1
0
0
0
1
2
3
2
3
0
0
0
4
5
,
4
5
6
0
0
0
6
7
8
9
1
0
C
D
là các m
a trận
tam
giác.
Nội Dung Chính
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