9-3 ?╅櫍?勬暩瀛搁?绠?

痻皚搭籔秖Scalar搭摸斑璶―琌┪搭痻皚ゲ惠ㄣΤ蝴璝蝴ぃ璓玥 MATLAB 穦玻ネ岿粇癟ㄒ

Example 1: 09-痻皚矪瞶籔笲衡/matrix12.mA = [12 34 56 20]; B = [1 3 2 4]; C = A + B C = 13 37 58 24

璝璶秈︽痻皚籔秖搭埃猭琌钡盢秖甶秨莱ノ痻皚–じ絛ㄒ

Example 2: 09-痻皚矪瞶籔笲衡/matrixAndScalarOperation.mA=[1 3 5]; fprintf('A = '); disp(A); fprintf('A+5 = '); disp(A+5); fprintf('A-3 = '); disp(A-3); fprintf('2*A = '); disp(2*A); fprintf('A/3 = '); disp(A/3); A = 1 3 5 A+5 = 6 8 10 A-3 = -2 0 2 2*A = 2 6 10 A/3 = 0.3333 1.0000 1.6667

Hint
瓃絛ㄒㄒ薄猵穦祇ネ秖埃痻皚ㄒ 5/A硂摸埃猭盢尿彻竊癚阶

璝饼秈︽痻皚ゲ惠絋粄材痻皚︽计ヘ Column Dimension ゲ惠单材痻皚绢计ヘRow Dimension玥礚猭秈︽痻皚MATLAB 穦玻ネ岿粇癟琌痻皚虏虫絛ㄒ

Example 3: 09-痻皚矪瞶籔笲衡/matrix13.mA = [1; 2]; B = [3, 4, 5]; C = A*B C = 3 4 5 6 8 10

痻皚埃猭盽虑パは痻皚┪秆絬┦よ祘Αㄓ笷Θ把ǎセ﹏ゝMATLAB祘Α砞璸秈顶絞材せ彻絬┦计材竊の材竊

痻皚Ωよ笲衡パ^ㄓ笷Θ痻皚ゲ惠琌よ皚ㄤΩよ笲衡Τ種竡ㄒ

Example 4: 09-痻皚矪瞶籔笲衡/matrix14.mA = magic(3); B = A^2 B = 91 67 67 67 91 67 67 67 91

璝*/の^ぇ玡翴MATLAB 盢穦磅︽痻皚ずじ癸じElement-by-element 笲衡ㄒ

Example 5: 09-痻皚矪瞶籔笲衡/elByEl01.mA = [12; 45]; B = [2; 3]; C = A.*B % 猔種*玡翴 D = A./B % 猔種/玡翴 E = A.^2 % 猔種^玡翴 C = 24 135 D = 6 15 E = 144 2025

癸狡计痻皚 zㄤ砿锣竚痻皚Conjugate Transpose ボΘ痻皚 z'ㄒ

Example 6: 09-痻皚矪瞶籔笲衡/conjTranspose01.mi = sqrt(-1); % 虫店计 z = [1+i, 2; 3, 1+2i]; w = z' % 砿锣竚猔種 z 虫ま腹 w = 1.0000 - 1.0000i 3.0000 + 0.0000i 2.0000 + 0.0000i 1.0000 - 2.0000i

璝稱眔ヴ痻皚 z 锣竚Transpose玥ボΘ痻皚 z.'ㄒ

Example 7: 09-痻皚矪瞶籔笲衡/transpose01.mi = sqrt(-1); % 虫店计 z = [1+i, 2; 3, 1+2i]; w = z.' % 虫锣竚猔種 z 翴の虫ま腹 w = 1.0000 + 1.0000i 3.0000 + 0.0000i 2.0000 + 0.0000i 1.0000 + 2.0000i

璝 z 龟计玥 z' ㎝ z.' 挡狦琌妓盽デ岿粇穦а痻皚 z 琌狡计盢 zˇ 粇粄琌虫痻皚锣竚

秖 a  Lp-norm ﹚竡 $$ \|a\|_p = \left(\sum_i |a_i|^p \right)^{1/p} $$

讽 p=2 秖 a ┪嘿稼んEuclidean Length饼―秖 Lp-normㄏノ norm ㄤㄏノ粂猭

norm(x, p)

絛ㄒ

Example 8: 09-痻皚矪瞶籔笲衡/normVector01.ma = [3 4]; x = norm(a, 1) y = norm(a, 2) z = norm(a, inf) x = 7 y = 5 z = 4

Hint
琌靡单Α
  • norm(a, 1)=$\sum_i |a_i|$
  • norm(a, inf)=$max_i |a_i|$

痻皚 A  p-norm ﹚竡 $$ \|A\|_p = max_x \frac{\|Ax\|_p}{\|x\|_p} $$

MATLAB  norm ョノ璸衡痻皚 p-normㄒ

Example 9: 09-痻皚矪瞶籔笲衡/normMatrix01.mA = [1 2 3; 4 5 6; 7 8 9]; norm(A, 2) ans = 16.8481

MATLAB 临Τ讽Ч俱计厩ㄧ计のàㄧ计常莱ノ秖の痻皚盢计厩ㄧ计俱瞶

ㄧ计弧
abs(x) 秖荡癸┪秖
angle(z) 狡计 z àPhase Angle
sqrt(x) 秨キよ
real(z) 狡计 z 龟场
imag(z) 狡计 z 店场
conj(z) 狡计 z 砿狡计
round(x) 彼き程俱计
fix(x) 礚阶タ璽彼计程俱计
floor(x) 狾ㄧ计彼タ计程俱计
ceil(x) ぱ狾ㄧ计タ计程俱计
rat(x) 盢龟计 x てだ计ボ
rats(x) 盢龟计 x て兜だ计甶秨
sign(x) 才腹ㄧ计Signum function$sign(x)=\left\{\begin{matrix}-1, x<0\\0, x=0\\1, x>0\end{matrix}\right.$
rem(x,y) ― x 埃y緇计
gcd(x,y) 俱计 x ㎝ y 程そ计
lcm(x,y) 俱计 x ㎝ y 程そ计
exp(x) 礛计
pow2(x) 2 计
log(x)  e ┏癸计礛癸计
log2(x)  2 ┏癸计
log10(x)  10 ┏癸计

盽ノàㄧ计俱瞶

ㄧ计弧
sin(x) タ┒ㄧ计
cos(x) 緇┒ㄧ计
tan(x) タちㄧ计
asin(x) はタ┒ㄧ计
acos(x) は緇┒ㄧ计
atan(x) はタちㄧ计
atan2(x,y) 禜はタちㄧ计
sinh(x) 禬禫タ┒ㄧ计
cosh(x) 禬禫緇┒ㄧ计
tanh(x) 禬禫タちㄧ计
asinh(x) は禬禫タ┒ㄧ计
acosh(x) は禬禫緇┒ㄧ计
atanh(x) は禬禫タちㄧ计

MATLAB 临Τㄇㄧ计琌皐癸秖じ参璸秖τ砞璸ㄒ min―秖伐mean―秖キА单俱瞶

ㄧ计弧
min(x) 秖 x じ程
max(x) 秖 x じ程
mean(x) 秖 x じキА
median(x) 秖 x じい计
std(x) 秖 x じ夹非畉
diff(x) 秖 x 綟じ畉
sort(x) 癸秖 x じ秈︽逼Sorting
length(x) 秖 x じ计
norm(x) 秖 x 稼んEuclidean
sum(x) 秖 x じ羆㎝
prod(x) 秖 x じ羆縩
cumsum(x) 秖 x 仓璸じ羆㎝
cumprod(x) 秖 x 仓璸じ羆縩
dot(x, y) 秖 x ㎝ y ず縩
cross(x, y) 秖 x ㎝ y 縩

ㄒsort 癸秖じ秈︽逼Sorting

Example 10: 09-痻皚矪瞶籔笲衡/sort01.mx = [3 5 8 1 4]; [sorted, index] = sort(x) % 癸痻皚 x じ秈︽逼 sorted = 1 3 4 5 8 index = 4 1 5 2 3

ㄤい sorted 琌逼秖index 玥琌–逼じ秖 x 竚传杠弧x(index) 单 sorted 秖Τ届拜肈ㄏノ sort 玡ㄒい sorted の index ㄓ―眔秖 x肈碞痙倒弄絤

瓃ㄧ计场続ノ痻皚琌盢痻皚跌︽秖栋ㄓ硋癸︽秖秈︽笲衡ㄒ饼т痻皚程じ竚块

Example 11: 09-痻皚矪瞶籔笲衡/max01.mx = magic(5); [colMax, colMaxIndex] = max(x) colMax = 23 24 25 21 22 colMaxIndex = 2 1 5 4 3

ㄤい colMax –︽程colMaxIndex 玥琌–︽瞷程竚璝璶―眔 x 程じ竚块

Example 12: 09-痻皚矪瞶籔笲衡/max02.mx = magic(5); [colMax, colMaxIndex] = max(x); [maxValue, maxIndex] = max(colMax); fprintf('Max value = x(%d, %d) = %d\n', ... colMaxIndex(maxIndex), maxIndex, maxValue);Max value = x(5, 3) = 25

パ痻皚 x 程じ琌 maxValueτㄤ祇ネ竚 [colMaxIndex(maxIndex), maxIndex] = [5 , 3]

Hint
璝璶т痻皚 x 程块 max(max)┪琌 max(x())


MATLAB祘Α砞璸絞