When data from a table (or tables) needs to be manipulated, easier to deal with info in form of a...
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Transcript of When data from a table (or tables) needs to be manipulated, easier to deal with info in form of a...
When data from a table (or tables) needs to be manipulated, easier to deal with info in form of a matrix.
Matrices
Fresh Soph Jun Sen
A 0 3 4 2
B 0 4 4 7
C 2 1 0 6
D 1 3 2 2
F 1 2 1 0
Terminology
Entry: The individual pieces of data in the matrix are called entries.
The entry in the ith row and jth column is:
The diagonal entries occur when i = j.
From previous matrix:
Order: If a matrix has m rows and n columns, then the matrix has an order of
Special Matrices
Identity: A square matrix with 1 for each diagonal entry and 0 for each non-diagonal entry. (written as I)
Square: A matrix with m=n.
Zero: A matrix with all entries = 0.
Special Matrices – continued
Row: A matrix of order 1 by n, also called a row vector.
Column: A matrix of order m by 1, also called a column vector.
Operations
Multiply a matrix by a non-zero constant.
531
012
032
A
Add two matrices of the same order.
Subtract two matrices of the same order.
101
617
520
B
16
15
14
C
BA BA C2
Balance of trade: A-B, exports - imports
A: US oil and coal exports to Canada, Germany, and France
B: US oil and coal imports from Canada, Germany, and France
Example 1
720
63.42
107.27
A
1317
8310
15.2
B
Power to influence: in a flow of information, who is the key?
otherwise
j odirectly t toinfo sends i if
0
1
ija
Create two matrices, A and B, with the following entries:
Example 2
otherwise
betweengo 1most at with j toinfo sends i if
0
1
ijb
1 2
3
4
5
otherwise
j odirectly t info sends i if
0
1
ija
Compute A+B. The row sum that is greatest in matrix A+B corresponds to person with most influence.
Example 2 – continued
otherwise
between-go 1most at with j toinfo sends i if
0
1
ijb
1 2
3
4
5