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MAT211 Lecture 17
Determinants.
Recall that a 2 x 2 matrix A
is invertible
If and only if a.db.c
!
0.
The number a.db.c is the the determinant of
A.
a
b
c
d
Definition
A
pattern
in an n x n matrix A is a
choice of entries of A, such that
there is only one entry in each row
and only one in each column.
Example
• Find all possible patterns in 2x2
matrices
• Find all possible patterns in 3x3
matrices.
• How many patterns are there in 4x4
matrices? And in n x n matrices?
Definition
The entries of a pattern P of a matrix A
are inverted if
one of them is located
right and above the other in A.
The signature of a pattern P of a matrix
A, denoted by sgn(P) is
(1)
(number of pairs of inverted entries in P)
EXAMPLE
• Find the signature of
the pattern of a
3 x 3 matrix A,
a
31
, a
22
, a
13
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View Full DocumentDefinition
The determinant a square matrix A,
denoted by det A is
"
sgn(P).product(elements in P)
where the sum is taken over all patterns
P.
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 Fall '08
 MOVSHEV
 Determinant

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