(1,)
[1 0]
1,
[1 0]
[,,,]
[0 0 0 0]
(,,,-2)
[0 0 0 -2]
(1;;2)
[1 0 2]
(1,1)
[1 1]
((1, 2), (4, 5))
[1 2; 4 5]
((1; 2; 3); (4; 5; 6))
[1 2 3; 4 5 6]
[[1, 2], [4, 5]]
[1 2; 4 5]
( 1; 2; 3, 4, 5, 6 ); (4; 5)
([1 2 3 4 5 6], [4 5])
[-0.1, 1.23, ], [.1, , -.2], [,,]
[-0.1 1.23 0; 0.1 0 -0.2; 0 0 0]
(1; 2; 3) * 2 - 2
[0 2 4]
adj([1 2; 4 5])
[5 -2; -4 1]
adj([1, 2, 3; 4, 5, 6; 1, 0, 9])
[45 -18 -3; -30 6 6; -5 2 -3]
adj([3 4 7 9; 5 4 -1 4; 8 7 8 5; 4 3 0 9])
[240 264 -177 -259; -284 -436 194 370; 16 100 -53 -31; -12 28 14 -54]
cofactor([1 2; 4 5], 1, 1)
5
cofactor([1 2 3; 4 5 6; 1 0 9], 1, 2)
-30
cofactor([3 4 7 9; 5 4 -1 4; 8 7 8 5; 4 3 0 9], 4, 4)
-54
columns([])
0
columns([1])
1
columns([1 2; 4 5])
2
#columns([1; 4 5 6; 1 9])
# 3
columns([[,,,]])
4
matrix(1, 1, [2])
2
matrix(1, 3, 2)
[2 0 0]
matrix(3, 1, [1 2])
[1; 2; 0]
matrix(3, 3, [])
[0 0 0; 0 0 0; 0 0 0]
matrix(3, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
[1 2 3; 4 5 6; 7 8 9]
vector()
[]
vector(,)
[0 0]
vector(1, 2, 3)
[1 2 3]
matrix2vector([[0]])
0
matrix2vector([1 2; 4 5])
[1 2 4 5]
matrix2vector([1 2 3; 4 5 6; 7 8 9])
[1 2 3 4 5 6 7 8 9]
horzcat([1], [2 3], [4 5 6 7])
[1 2 3 4 5 6 7]
horzcat([1; 2], [3 4; 5 6], [7 8 9; 10 11 12])
[1 3 4 7 8 9; 2 5 6 10 11 12]
vertcat([1 2], [3 4], [5 6])
[1 2; 3 4; 5 6]
((1; 2; 3); (4; 5; 6)) * ((7; 8); (9; 10); (11; 12))
[58 64; 139 154]
cross((1; 2; 3); (4; 5; 6))
[-3 6 -3]
det([[1]])
1
det([1 2; 4 5])
-3
det([1 2 3; 4 5 6; 1 0 9])
-30
det([3 4 7 9; 5 4 -1 4; 8 7 8 5; 4 3 0 9])
-412
dimension([])
0
dimension([0])
1
dimension([1 2 3 4])
4
dot((2); (3))
6
dot((1; 2); (3, 4))
11
dot((1; 2; 3); (4; 5; 6))
32
(1; 2; 3).(4; 5; 6)
32
(1; 2; 3, 4) . (5; 6; 7, 8)
70
element([1 2; 3 4], 1)
[1 2]
element([1 2 3; 4 5 6; 1 0 9], 1, 3)
3
element([1 2 3; 4 5 6], 2, 1)
4
multiply(1)
1
multiply([1 2; 4 5], 2)
[2 4; 8 10]
[1 2; 4 5] * 2
[2 4; 8 10]
multiply([1 2], 3, 4)
[12 24]
[1 2] times 3 times 4
[12 24]
[1 2].*[3 4]
[3 8]
[1; 2].*[3 4]
[3 4; 6 8]
[1 2; 3 4].*[1 2; 3 4]
[1 4; 9 16]
pow([1 2; 3 4], 2)
[1 4; 9 16]
[1 2; 3 4].^2
[1 4; 9 16]
[2 4; 3 4].^[-1; 2]
[0.5 0.25; 9 16]
[2; 3].^[3 4]
[8 16; 27 81]
[2 4 12] / 2
[1 2 6]
divide([2 4 12], 2)
[1 2 6]
[2 4 12]./2
[1 2 6]
[[2, 4], [6, 12]] / 2
[1 2; 3 6]
[2 4; 6 12]./[1 2; 3 4]
[2 2; 2 3]
elements([])
0
elements([1 2])
2
elements([1 2; 3 4])
4
entrywise(x, [4 10 12], x)
[4 10 12]
entrywise(x / y, [4 10 12], x, [2 2 4], y)
[2 5 3]
entrywise(x / y + z, [4 10 12], x, [2 2 4], y, [1 2 3], z)
[3 7 6]
column([1], 1)
1
column([1, 2], 1)
1
column([1 2; 3 4], 2)
[2 4]
row([1], 1)
1
row([1 2], 1)
[1 2]
row([1 2; 3 4], 2)
[3 4]
genvector(x+10, 1, 2, 2)
[11 12]
genvector(x+10, 1, 2, 3)
[11 11.5 12]
genvector(x+10, -1, 2, 5)
[9 9.75 10.5 11.25 12]
genvector(x+10, -1, 2, 7, x, 0)
[9 9.5 10 10.5 11 11.5 12]
genvector(x+100, -3, 5, 2, x, 1)
[97 99 101 103 105]
genvector(x+100, 1, 2, 1, y, 1)
[(x + 100) (x + 100)]
hadamard([2], [3], [4])
24
hadamard([1 2 3; 4 5 6]; [7 8 9; 10 11 12])
[7 16 27; 40 55 72]
identity(1)
1
identity(3)
[1 0 0; 0 1 0; 0 0 1]
identity([1 2; 4 5])
[1 0; 0 1]
magnitude(-2)
2
magnitude([-2])
2
magnitude([-2, 3, 4])
5.385164807
part([1], 1, 1, 1, 1)
1
part([1 2 3; 4 5 6; 7 8 9; 10 11 12], 2, 2, 2, 2)
5
part([1 2 3; 4 5 6; 7 8 9; 10 11 12], 1, 3, 2, 3)
[3; 6]
part([1 2 3; 4 5 6; 7 8 9; 10 11 12], 1, 2, 4, 3)
[2 3; 5 6; 8 9; 11 12]
((1; 2); (3; 4))^-1
[-2 1; 1.5 -0.5]
inverse([1 2; 3 5])
[-5 2; 3 -1]
inverse([1 2 3; 4 5 6; 1 0 9])
[-1.5 0.6 0.1; 1 -0.2 -0.2; 0.1666666667 -0.06666666667 0.1]
inverse([1 1 1 1; 2 4 -1 4; 2 4 3 4; 4 3 0 2])
[2 0.125 -0.625 0; -6 -0.75 1.75 1; 0 -0.25 0.25 0; 5 0.875 -1.375 -1]
rk([1 2 3; 3 6 9])
1
rk([1 2 3; 0 2 2; 1 4 5])
2
rk([1 2 3; 0 2 2; 1 -2 -1])
2
rk(identity(3))
3
combine([1, 2])
[1 2]
combine([1, 2], [3], [4, 5, 6])
[1 2 3 4 5 6]
norm([2])
2
norm([3, 4])
5
norm([2, 3, 6])
7
permanent([1])
1
permanent([1 2; 4 5])
13
permanent([1 2 3; 4 5 6; 1 0 9])
144
permanent([3 4 7 9; 5 4 -1 4; 8 7 8 5; 4 3 0 9])
11028
rank([6, 7, 1, 4])
[3 4 1 2]
rank([-1, 2, 5, 10], 1)
[1 2 3 4]
rank([-1, 2, 5, 10], 0)
[4 3 2 1]
rref([1 3 1 9; 1 1 -1 1; 3 11 5 35])
[1 0 -2 -3; 0 1 1 4; 0 0 0 0]
rows([1])
1
rows([1 2; 3 4])
2
sort([5, 2, 0, 1, 3, -4, 0])
[-4 0 0 1 2 3 5]
sort([5, 2, 0, 1, 3, -4, 0], 1)
[-4 0 0 1 2 3 5]
sort([5, 2, 0, 1, 3, -4, 0], 0)
[5 3 2 1 0 0 -4]
transpose([1 2; 3 4])
[1 3; 2 4]
[1 2 3; 4 5 6].'
[1 4; 2 5; 3 6]
slice([5], 1, 1)
5
slice([5, 6, 7, 8, 9], 2, 4)
[6 7 8]