• Tiada Hasil Ditemukan

Some studies on the geometry of block triangular matrices

N/A
N/A
Protected

Academic year: 2022

Share "Some studies on the geometry of block triangular matrices"

Copied!
22
0
0

Tekspenuh

(1)

PERPUSTAKAAN UNIVERSITI MALAYA

International Conference on Rings and Algebras (10-16 July 2011 :Taipei, Taiwan).

1) Some studies on the geometry of block triangular matrices, by Chooi Wai Leong.

2) Bounded distance preserving surjective mappings on block triangular

matrix algebras, by Chooi Wai Leong.

(2)

PERPUSTAKAAN UNIVERSITI MALAYA

-

Some studies on the geometry of block triangular matrices

Chooi Wai Leong

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Abstract

Inthis talk, we will present some latest studies of surjective mappings preserving bounded distance in both directions on matrix spaces, which is an continuation study of adjacency preserving mappings. Some recent works on surjective mappings preserving bounded distance in both directions on block triangular matrix algebras will be discussed.

E-mail address:wlchooi@um.edu.my

(3)

c::

o

c, ..!:o

.:::.!VI

~

..!:

...

I

1.0

<II ..!:

I-

o

(4)

.... o

Q)s:::

o

.!!!

Q)

us:::

(1)

.!!!+-'

"0

'+-

o

II) +-'s:::

'0

ro

0.

E

o

s:::

~ E

n

(5)

j

IiI

(6)

<lI ,~

c:

4=c:

"'C

c:ra

<lI ,~

c:

4=

...

o

If)

::Jo

'':::

ra>

c:

"'C

<lI

'0 ...::J

If)

c

:!l iG

..c u

<lI ra

> Q.

ra If)

.I: ...

If) ra

E ~

<lI

::0-

e ~

Q. 0

lo.,. 'in

ra c:

,_ <lI

E E

'iii '0

c:

..c

al

If)

ra

.I:

'C

~

...

ra

E

'0 z-

~ E ..

o If)

<II c:

bOO

~ '"5, ... E

... ::J

o ~

E

ra

<lI ...

o~

<lI ra

.I: <lI

~ 3:

ra ...

... <lI c:"'C

<lI c:

E

::J

.g~

c: >

.2 e

<II Q.

£ E

• •

o

(7)

"'0

Q)

"'0

c::

::J

o

co

eo c::

c:

IJ)

Q)

c::

IJ)

0

Q) .-

~ +-'

0.. ~

~

IJ) .-

bOO c::

.- ..c

c..+-,

c.. 0

ro

((l

~ c

o

,,~

Q)

>

Q)

.~

U

~

U

c

5

Q)

ro

«

'2

+-'

~

IJ)

::J

0

l- V)

(/)

a:

w 2: z

:::>

z -c

~ ~

(/)

:::>

c,

a:

UJn,

(8)

"

..

n

(9)
(10)

>'bO

.0 c:::

I"

o

(11)

• •

o

(12)

(j if

<;'

c: ~I

~

..s::::(l)

~

.s:... "'0

I.J

...

0 (l)

.;::

....

"'0 Q)I.J ..c "'0c: "'0

'11 (l) c: c: c:

E

>0

...

ro N ::l0 ro

"-

....

.!!!

..._

.0 I/)

0 c.

" ~

(l)

C

"'0

"

Q) bec:

.

u.:

~

....

Q) c:ro

"

Q) uc:

z ...

ro

E

..s:::: c:::l ...ro (l)

E

~

c. 0 .!!! I/)(l) 0

ro ..c

" ....

c:

....

c. .~

be

" "

Q) Q) Q) I/)

.~

":S

NM (l)U '+=X '+=x be

E

"I:l N c: c: ....

I '11 '11 ._ (l)

t:: .-I ro §::r:

'11 N

...

bD bD

11) N .!!! c: c: ro c:

..c: ... "'0

.~ .~ E

0

0..0

...

....

~ .-I "'0 c: Q) Q) (l) (l)

(l) 0 III III

C. bO~ ...5!! Q) Q) > u

0

... ... .

.;::; c:

ro

~

be ro a. a.

c. Q)I.J

~ .~

E bD bD u(l) ...ro

t:: ro ::l .,..., I/)

.!!! '11

~

c: c:

... _

od" '+- CT .!!! .is.. .is.. ::l "'0

..s::::

....

0 (l)

~

:5

a. a. a. I/)

~

c: "I:l

c..

a.

...

C.(l) (l)

....

ro ....0E '11E roE "'0(l) X

bO 0

«

u I/) 0 Q) Q)

.

N.:t.;:: vi

c:

~

c: c: .!!! > vi > (l) I/) (l)

ro::l _ ..ctil.... 0u

.-e

0

~

.,.:;u .2c: ",.:;u

...

u '11

.

U.:

:r:

bDc: Q)bD (l) a. Q) ... Q) ro Qj

...

..s:::: (l) '11 .~ U

.~

vi

....

~

ro

~

'11::l

« ...

I/)I/)

....

bD

~ .~

::lIII c:0 ..s::::ro

E

_j

:::r: ....

'11 "'0(l) ro ro

'11"

'11 .,.:; U I/)ro u

1Il~ U (l)

.

.:

a.:

Q)c: u bec: .!!!

.- ...

.!!! Q)

....

..s:::: (l)

...

0 ::J

~_g

U (l)

...-4 _j :J "'0

.~ ~ ~ "

c:- c:

E

0 0 ro

Nc:

• ... ...

c:

..g • • •

..s::::(l)

.~ E

>.

f- "'0 I/)

(13)

Vl

~

U

~

';:

ro ~c.. ro

Vl

E

."

o

(14)

vc:

v

.0 V>

.c:cv

IIIV

".:U

.j...I

cv

E

,",

o

• • •

(15)

.::L.

U

o

:::0

~

'_;:j V1'" ra

c: eo ~ V1

o

C:::S <11

U

'c..

boO

£

ra a. c:

V1 ra .~

« E ,;;

.::L.

U

o

:::0

~ x

"0

c:ra

<11

c:

o

.!!!

c:

o

'_;:j

ra

b

c:

<11

o E

V1

"0

<11

<11

c:

~

<11 V1

o

..c:

~

c:

o

'&'j

::su .!!!

"0 <11 Ura a.

V1 Q)

..c:

...

.!!!

....

::s

... o o

.... o

u,

• • •

...

o

""'..

t-f

..cra

...

~

..cra ::sV1

·CX

...

ra

E

~ It)

..c:

...

-5

0

::sV1 t:

.VI

....,

VI

(16)

VI

CO

I

'<:(

'-"

~

~II

u

(17)

be

rn

.S

QJ

QJ

(.J 0..

>

... ,... g.~

1e

>,

S ~

s..o o:t

~

0..

~'i Lf1 ... ....

-~

---.o:t

....

(.J

g

~~ ~

:::?QJ [1

I ..0 0

.~ ... ~

It)

....

cO"l:l

,... 0..

~ .23~

~g.

'-'"

~

...

§OS +

.... ::l

It) cOP:)

QJ

u1

...c:I

Ln...c:l

.... LO

....

---.

X It) QJ -

QJ

....

.... o;t

Ln..o

~

0

II

'a~

I

s:l

~

QJ '- ~

C'C!

i

~ ,...0

] .s ...

'-'"

. ....

QJ~

+

~---,(.J

~

..-t QJ

cO ., '0::(

w

'-'.!:l

Ji~ II

s:l"l:l

~~...c:I

....

~

---.

~:a~

E..:l

...

'0::(

II

s:l..o

g-d ~ o

s:l

QJ-

'0::( (.J ...

"l:lJl

e;.bOC

~cO QJSs:l

>

QJ

....

QJ

,...

QJ

.23 ~

~

..:l 4=<

t31e:.&

rn C'C!

o

(18)

ro

...

..0 Q)

~

ro ..0 ::l Vl

X Q)

·C C

+-'U::

ro Q)

E"O

ro ~

::l

~ ~

.!:!!~

... ~ ...

..::t:. 0

gV) :0&1

ro..o

Q) ::l

..0 Vl

.:.:Z'

.:: a.

~E

Q)

~ §

"0 C C..J:

ro u

t:: ~

VI

0

... u.

VI

t:

.-1<

....J

~~

0

...VI

><

I .__,l-

~

II

"0 C

ro

II

~"

n

(19)

.--.

c::

'-"

~ E

V

~

VI

-e II

~

en

I

'-"

<::4

VI

...

::§ ~

.~ ~ ...

E

CIJ ...Q

~

~

UJ

en

~

... "'0

CIJ c::

-J !11

...

c:: c::

'-" '-"

"'0 "'0 c:: c::

!11 !11

N M

v'

II II /\\

-c::

-e

..c::

• • •

o

(20)

II)

II

(21)

~.. N II II -e

-t::

• •

II

n

II

(22)

II

II

~ ...

t::

--

~..:: 12 ,.:;; ":;;N- ';;N

"'!_ "'!_ II "'!_ II

...

'"'"

M-

-S-S ~-S ~

II •• •

~,

D

Rujukan

DOKUMEN BERKAITAN

As a conclusion of the thesis, in this research, we study the classical adjoint- commuting mappings on various types of matrices such as full matrices, hermitian matrices,

Secondly, for each of the five interesting function fields introduced in Chapter 3, we work out an explicit basis for a specific Riemann-Roch space for one-point AG

Some important factors which emerge from the above reviewed studies inform the present study. All the previous studies reviewed in this chapter generally reported the preference of

Keywords: Per-alternate triangular matrices, bijective adjacency invariant maps, rank-2 preservers..

Bounded distance preserving surjective mappings on block triangular matrix algebras.. Chooi

H1: There is a significant relationship between social influence and Malaysian entrepreneur’s behavioral intention to adopt social media marketing... Page 57 of

Based on the previous studies on refusals in different languages and some speech acts in Persian it is hypothesized that Iranian speakers of Persian will use more indirect

present work, template-free, and one-step process was used to synthesize a silica supported sulfonic acid catalyst, using rice husk ash (RHA) as a cheap source of silica,