Day la 1 ma tran chuyen vi (transposed matrix). Mot cach khac de tao 1 ma tran hoan vi la dung t().

Ma tran vo huong (scalar matrix) la mot ma tran vuong (tuc so dong bang so cot), va tat ca cac phan tu ngoai duong cheo (off-diagonal elements) la 0, va phan tu duong cheo la 1.

#Tao ra 1 ma tran 3x3 voi tat ca cac phan tu la O. 
A=matrix(0,3,3)
# Cho cac phan tu duong cheo bang 1
diag(A) = 1
diag(A)

## [1] 1 1 1

##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1

IV.1) Chiet phan tu tu ma tran

y=c(1:9)
A=matrix(y,nrow=3)
A

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

# Cot 1 cua ma tran A
A[,1]

## [1] 1 2 3

# Cot 3 cua ma tran A
A[,3]

## [1] 7 8 9

# Dong 1 cua ma tran A
A[1,]

## [1] 1 4 7

# Dong 2, cot 3 cua ma tran A
A[2,3]

## [1] 8

# Tat ca cac dong cua ma tran A, ngoai tru dong 2
A[-2,]

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    3    6    9

# Tat ca cac cot cua ma tran A, ngoai tru cot 1
A[,-1]

##      [,1] [,2]
## [1,]    4    7
## [2,]    5    8
## [3,]    6    9

#Xem phan tu nao cao hon 3
A>3

##       [,1] [,2] [,3]
## [1,] FALSE TRUE TRUE
## [2,] FALSE TRUE TRUE
## [3,] FALSE TRUE TRUE

IV.2) TINH TOAN VOI MA TRAN * Cong va tru 2 ma tran

A=matrix(1:12., 3,4)
B=matrix(-1:-12, 3,4)
A

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

##      [,1] [,2] [,3] [,4]
## [1,]   -1   -4   -7  -10
## [2,]   -2   -5   -8  -11
## [3,]   -3   -6   -9  -12

C=A+B
D=A-B
C

##      [,1] [,2] [,3] [,4]
## [1,]    0    0    0    0
## [2,]    0    0    0    0
## [3,]    0    0    0    0

##      [,1] [,2] [,3] [,4]
## [1,]    2    8   14   20
## [2,]    4   10   16   22
## [3,]    6   12   18   24

Nhan hai ma tran Chung ta co 2 ma tran A va B

A=matrix(1:9, 3, 3)
B=t(A)
A

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9

Chung ta tinh AxB bang lenh "%*%"

AB =A%*%B
AB

##      [,1] [,2] [,3]
## [1,]   66   78   90
## [2,]   78   93  108
## [3,]   90  108  126

Hay tinh BxA

BA=B%*%A
BA

##      [,1] [,2] [,3]
## [1,]   14   32   50
## [2,]   32   77  122
## [3,]   50  122  194

*Nghich dao ma tran va giai he phuong trinh

A=matrix(c(3,1,4,6), nrow=2)
Y=matrix(c(4,2), nrow=2)
X=solve(A)%*%Y
X

##           [,1]
## [1,] 1.1428571
## [2,] 0.1428571

#Chung ta co the kiem tra 
3*X[1,1]+4*X[2,1]

## [1] 4

Tri so eigen cung co the tinh toan bang function eigen nhu sau:

eigen(A)

## eigen() decomposition
## $values
## [1] 7 2
## 
## $vectors
##            [,1]       [,2]
## [1,] -0.7071068 -0.9701425
## [2,] -0.7071068  0.2425356

DINH THUC (Determinant) De xac dinh mot ma tran co the dao nghich hay khong: Ma tran ma dinh thuc bang 0 la ma tran suy bien (singular matrix), va khong the dao nghich. De kiem tra dinh thuc, R dung lenh det()

E=matrix((1:9),3,3)
E

##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

det(E)

## [1] 0

Nhung ma tran F sau day thi co the dao nghich

F=matrix((1:9)^2, 3, 3)
F

##      [,1] [,2] [,3]
## [1,]    1   16   49
## [2,]    4   25   64
## [3,]    9   36   81

det(F)

## [1] -216

Va nghich dao cua ma tran F (F^-1) co the tinh bang function “solve()”

solve(F)

##           [,1]      [,2]       [,3]
## [1,]  1.291667 -2.166667  0.9305556
## [2,] -1.166667  1.666667 -0.6111111
## [3,]  0.375000 -0.500000  0.1805556

R co 1 package Matrix chuyen thiet ke cho tinh toan ma tran va TLTK di kem.

4. Dung R cho cac phep tinh don gian va ma tran_2/2

NVT_BH

3/29/2020

Ma tran vo huong (scalar matrix) la mot ma tran vuong (tuc so dong bang so cot), va tat ca cac phan tu ngoai duong cheo (off-diagonal elements) la 0, va phan tu duong cheo la 1.