Matlab ��𣂷�𥕢�鈭𥟇�䁅膩蝯梯����遆撘譌�����𡠺蝮賢�� sum����憭批�� max����撠誩�� min��
撟喳��彍 mean��銝凋�齿彍 median����𡝗見璅蹱�硋榆 std��
>> x = [4 9 0 4 1 10 3 8];
>> sum(x)
ans =
39
>> max(x)
ans =
10
>> min(x)
ans =
0
>> mean(x)
ans =
4.8750
>> std(x)
ans =
3.7201
�嗘�𥟇�䁅膩蝯梯��遆撘誩虾隞乩�𦦵鍂�銁��煾�譌��摨誩�𦯀�𠺪���嗆�讐儔�㮾��䎚��
雿��糓憒���靝�𦦵鍂�銁�畆�腼銝𠺪�峕�𤩺�脲糓撠滨畆�腼銝剔�瘥譍�銵��𡁶絞閮���𤩺�腈��
>> A = [4 6; 9 6; 0 2; 4 8; 1 0; 10 10; 3 7; 8 7]
A =
4 6
9 6
0 2
4 8
1 0
10 10
3 7
8 7
>> sum(A)
ans =
39 46
>> max(A)
ans =
10 10
>> mean(A)
ans =
4.8750 5.7500
銝��贝��絞閮��𧼮虜�㮾��𦦵��遆撘𤩺糓��鍦�� sort��Matlab �蘨撠齿彍�潭�鍦�𧶏��
�䔶�𥪜�摰𡁏糓敺𧼮�𤩺�鍦�憭扼��憒���靝�𦦵鍂�銁�畆�腼銝𠺪�峕�𤩺�脲糓撠��譍�銵���ê̌��鍦�譌��
>> sort(x)
ans =
0 1 3 4 4 8 9 10
>> sort(A)
ans =
0 0
1 2
3 6
4 6
4 7
8 7
9 8
10 10
憒���𡏭�撠滚�堒�𡁶絞閮��𡝗�鍦�誩𢅛嚗罸��虾隞亙���嗘�𥕦遆撘譍�𦦵鍂�銁頧厩蔭�畆�腼銝𨳍��
Matlab ��頧厩蔭蝚西��糓 '
>> x'
ans =
4
9
0
4
1
10
3
8
>> A'
ans =
4 9 0 4 1 10 3 8
6 6 2 8 0 10 7 7
>> sort(A')
ans =
4 6 0 4 0 10 3 7
6 9 2 8 1 10 7 8
>> B = sort(A'); B'
ans =
4 6
6 9
0 2
4 8
0 1
10 10
3 7
7 8
銝���堒虾隞亙神�拙�衤誑銝羓����誘嚗����𦦵鍂����罸�娪�页�����漤𢒰�����誘銝滩撓�枂閮��㛖�鞉�栶��
憒���𦦵鍂�烾�鮋�娪�页�����漤𢒰�����誘頛詨枂閮��㛖�鞉�栶��
>> 1+1, 1+2; 1+3
ans =
2
ans =
4
�訜 Matlab �䔄�𣶹��閬��脣�亥��彍��毺����辷����䌊��閙��𠾼��
>> sqrt(-4)
ans =
0 + 2.0000i
憒���𡏭��䌊撌梯ˊ�㰘��彍嚗�虾隞亥牧
>> i=sqrt(-1); c = 2 + 3*i
c =
2.0000 + 3.0000i
��𤥁��
>> c = complex(2,3)
c =
2.0000 + 3.0000i
蝝娪�譍�条畆�腼���讐儔嚗峕糓撠��娪�讛��畆�腼銝剔�瘥誩�见��蝝删㮾銋塩����隞�
>> A = [1 2; 2 1]; B = [3 4; 5 6]; C = A + B*i
C =
1.0000 + 3.0000i 2.0000 + 4.0000i
2.0000 + 5.0000i 1.0000 + 6.0000i
�𣶹�銁��穃�𤏸��䰻�橒�愢atlab �� ' 蝚西�笔�嗅祕�糓�� Hermittian ���𤩺�嘅�䔶�滚蘨�糓頧厩蔭
>> C'
ans =
1.0000 - 3.0000i 2.0000 - 5.0000i
2.0000 - 4.0000i 1.0000 - 6.0000i
憒���𡏭��蘨�朞�厩蔭嚗峕�㕑府�鍂 .' 蝚西��
>> C.'
ans =
1.0000 + 3.0000i 2.0000 + 5.0000i
2.0000 + 4.0000i 1.0000 + 6.0000i
閮��堒�煾�讐�甇𣂼嗾����烾𩑈摨佗�諹秐撠烐�劐�厩車�䲮瘜訫虾�鍂��
>> sqrt(x * x')
ans =
16.9411
>> sqrt(dot(x,x))
ans =
16.9411
>> norm(x)
ans =
16.9411
�畆�腼�𧋦靘�瘝埝�厰膄瘜𤏪�䔶��糓憒���𨀣�厰���畆�腼���畆�腼�㮾銋条���敶ｇ��
Matlab �虾隞亙���撖急�鞾膄瘜𨰻��雿��糓��删�箇畆�腼銋䀹�閙�埝�劐漱��𥕦�页��
��隞亥�摰𡁶儔�拍車�䲮��𤑳��膄瘜𨰻��$A^{-1} B$ 撖怠�� A\B嚗�
�� $B A^{-1}$ 撖怠�� B/A���訜�塚�𣬚㮾銋㗛�蹱䲮���畆�腼蝬剖漲閬����聢��滩�賭�塩��
>> A=[-3 0 1; 2 5 -7; -1 4 8]
A =
-3 0 1
2 5 -7
-1 4 8
>> b=[1; 2; 3]
b =
1
2
3
�𥅾閬�瘙� A*x = b ��閫� x 嚗���糓
>> x = A\b
x =
-0.3194
0.5864
0.0419
��穃�穃虾隞交炎�䰻閮��㛖�畾㗛�� (residual)嚗峕釣�𧶏�䔶誑銝贝���㛖�銝齿糓隤文榆 (error)嚗�
蝝啁���坔��畆�腼閮��㛖�隤脣�滩����
>> A*x - b
ans =
1.0e-15 *
0
-0.4441
-0.4441
摰��煾�賣糓 $10^{-15}$ 撌血𢰧���彍嚗屸�嗘�𥟇彍撌脩�枏���𧶏���誩��虾隞亥�滨�箸糓 0 ���𧑐甇乓��
�彍�潸圾 x 撟曆�擧偶�牐�滚虾�賜�㗇䲰���迤��閫��𣬚蜇����劐�𥡝炊撌柴��
�訜畾㗛�誩���讐����辷�峕�穃�煾�𡁜虜撠梁㮾靽∟炊撌桐�笔���譌��
蝺𡁏�扯�舐�𧢲䲮蝔见�誩虾�賣�匧𣈲銝�閫����∟圾���∠狙憭𡁶�閫����瘜���
Matlab ���膄瘜𤏪��虾隞交�劐�䀹���厰�嗘�𤤿�瘜���
閰單��銋蠘���坔��畆�腼閮��烾���隤脫�滩�質����
�拙�讠雁摨虫�璅���畆�腼嚗�虾隞亦鍂 ./ �𡁜�齿�厰��㮾�膄��
>> [1 3 5] ./ [2 6 10]
ans =
0.5000 0.5000 0.5000
�嗅祕嚗𣬚�娪�讛��畆�腼銋钅�橒�䔶�笔虾隞亦鍂 ./ ��� *��+��- 蝚西�笔�𡁶陛靘輻�撠齿�厰��㮾�膄��
�㮾銋塩���㮾��𨬭���㮾皜䜘��
>> 1 ./ [1 2 3]
ans =
1.0000 0.5000 0.3333
>> 1 + [1 2 3]
ans =
2 3 4
>> [1 2 3] - 1
ans =
0 1 2
瘙����畆�腼���遆撘𤩺糓 inv嚗䔶��糓�膄瘜閖�讠�埈�娍����畆�腼閬���㗇�����堒�𠾼��
��隞伐�屸膄��䂿�訫�齿�匧�閬�嚗�炏����㕑府敺墧迨��韏瘀�諹牲閮矋�帋�滩��鍂 inv �遆撘譌��
�畆�腼���鸌敺萄�澆�𣬚鸌敺萄�煾�𧶏�屸�賢虾隞亦鍂 eig �遆撘𤩺�敺𨰜��
>> eig(A)
ans =
-2.8601
6.4300 + 5.0434i
6.4300 - 5.0434i
�蹱糓 A ��銝匧�讠鸌敺萄�潦��
>> [V,D] = eig(A);
��� D �糓銝��见�滩�垍�𡁶畆�腼嚗��嗅�滩�垍�𡁜��蝝惩停�糓 A ���鸌敺萄�潦��
�� V �糓銝��𧢲䲮�腼嚗����蝚� k 銵�停�糓撠齿�� D(k,k) ���鸌敺萄�煾�譌��
�鸌敺萄�煾�𤩺�厩�⊿�𣂼�𡁜�页�愢atlab ��𣇉��糓�𩑈摨衣�� 1 ��甇��� (normal) �鸌敺萄�煾�譌��
>> D
D =
-2.8601 0 0
0 6.4300 + 5.0434i 0
0 0 6.4300 - 5.0434i
>> V
V =
0.9823 -0.0055 + 0.0565i -0.0055 - 0.0565i
-0.1275 -0.5062 - 0.6094i -0.5062 + 0.6094i
0.1374 -0.3372 + 0.5054i -0.3372 - 0.5054i
瘙��畆�腼銵��堒�譌����擧彍 (rank)��撠滩�垍�𡁜�� (trace) �����誘���ê̌�糓 det, rank, trace��
隢贝����䌊撌勗祕撽𨰜��