ofect - o
Matrices
Cestaon
Jhe re ctangular elemetd
ano Columny mafrex
A a2n
am) amn JmX n
amn ne entre eg elementy
mX n
matX
determenant A, Jle Ocler
Colwhn
e. y m ant no
SPecil
|: Sure matre'x!
number n umber
matrx in which
Calleo a `yore matrrx
Colwm ns ane
Eamle:
*/3x3
a. Retanvlay Matx
number of ans and number of
Columns e Callee a, Rectonguloy natsx
2. Rouw matrx: afrix
A matrx haveng nly Caked
a motrK
tiampe
y. Coymn mn atrex: A mate'x hareng nyn Calunn
colwmn matrx.
, S. Diagnal matrx:
matox whee all the
man
Cale dtasnat matrx,
Example: A=
a22
ann
sealar ma;
matrx he tform
calleol Seorar matrex
Exampee
2
7. ldentity mari ( Unt motrix)
A Sayrne motrex diagonal
elenets ame I ano al non deagmal elemes ane O
ldetity matrcx,
Exanfale
UPper
8. UPper Trà angular matix! 4s math Ie -fm
és calle ther
Tn'angular matix ;
, (4) Lover Trcaglar matrix
Pormm
a32 a33 -
an
krianglar matre.
Called a Lower
2
(10) ldewpofeut motrc'x:
matrex &aiot to be dempofenl
Examle: ().
1. Symmetrcc Matrex : Sysm metrc
A Sqrone matrx A
Examle A-(9)
1a. SKew-Sym matrec matrx A
A 3qvae. matrex A is Baid to be Skew-Symmetec
Exompee : 4- (9 ).
B. Csnjugate f a matrx
Let A (oi) mxn ke amatrcx,
Yhen (ij) mn where
calleel te eonycegate ¢ matrix A. gt is enote
bgte
lu.
Hermiian
A matrix is Sa to de Hermùtian 4
whe
3
Matrices
Cestaon
Jhe re ctangular elemetd
ano Columny mafrex
A a2n
am) amn JmX n
amn ne entre eg elementy
mX n
matX
determenant A, Jle Ocler
Colwhn
e. y m ant no
SPecil
|: Sure matre'x!
number n umber
matrx in which
Calleo a `yore matrrx
Colwm ns ane
Eamle:
*/3x3
a. Retanvlay Matx
number of ans and number of
Columns e Callee a, Rectonguloy natsx
2. Rouw matrx: afrix
A matrx haveng nly Caked
a motrK
tiampe
y. Coymn mn atrex: A mate'x hareng nyn Calunn
colwmn matrx.
, S. Diagnal matrx:
matox whee all the
man
Cale dtasnat matrx,
Example: A=
a22
ann
sealar ma;
matrx he tform
calleol Seorar matrex
Exampee
2
7. ldentity mari ( Unt motrix)
A Sayrne motrex diagonal
elenets ame I ano al non deagmal elemes ane O
ldetity matrcx,
Exanfale
UPper
8. UPper Trà angular matix! 4s math Ie -fm
és calle ther
Tn'angular matix ;
, (4) Lover Trcaglar matrix
Pormm
a32 a33 -
an
krianglar matre.
Called a Lower
2
(10) ldewpofeut motrc'x:
matrex &aiot to be dempofenl
Examle: ().
1. Symmetrcc Matrex : Sysm metrc
A Sqrone matrx A
Examle A-(9)
1a. SKew-Sym matrec matrx A
A 3qvae. matrex A is Baid to be Skew-Symmetec
Exompee : 4- (9 ).
B. Csnjugate f a matrx
Let A (oi) mxn ke amatrcx,
Yhen (ij) mn where
calleel te eonycegate ¢ matrix A. gt is enote
bgte
lu.
Hermiian
A matrix is Sa to de Hermùtian 4
whe
3
