tangent
Not Supported
[
V
1
I
2
]
=
[
h
11
h
12
h
21
h
22
]
[
I
1
V
2
]
Search
Returned 88 matches (100 formulae, 59 docs)
Lookup 1.774 ms, Re-ranking 723.428 ms
Found 6405 tuple postings, 3764 formulae, 1739 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
5.3953
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Two-port_network.html
[
V
1
I
2
]
=
[
h
11
h
12
h
21
h
22
]
[
I
1
V
2
]
[
V
1
V
2
]
=
[
z
11
z
12
z
21
z
22
]
[
I
1
I
2
]
[
V
1
V
2
]
=
[
z
11
z
12
z
21
z
22
]
[
I
1
I
2
]
[
h
11
h
12
h
21
h
22
]
[
I
1
I
2
]
=
[
y
11
y
12
y
21
y
22
]
[
V
1
V
2
]
[
b
1
b
2
]
=
[
S
11
S
12
S
21
S
22
]
[
a
1
a
2
]
[
I
1
V
2
]
=
[
g
11
g
12
g
21
g
22
]
[
V
1
I
2
]
[
a
1
b
1
]
=
[
T
11
T
12
T
21
T
22
]
[
b
2
a
2
]
[
V
2
I
2
′
]
=
[
A
′
B
′
C
′
D
′
]
[
V
1
I
1
]
[
V
2
I
2
′
]
=
[
1
-
R
-
s
C
1
+
s
C
R
]
[
V
1
I
1
]
[
V
1
I
1
]
=
[
A
B
C
D
]
[
V
2
-
I
2
]
[
a
11
a
12
a
21
a
22
]
[
b
11
b
12
b
21
b
22
]
[
g
11
g
12
g
21
g
22
]
[
y
11
y
12
y
21
y
22
]
[
z
11
z
12
z
21
z
22
]
[
V
1
V
2
V
3
]
=
[
Z
11
Z
12
Z
13
Z
21
Z
22
Z
23
Z
31
Z
32
Z
33
]
[
I
1
I
2
I
3
]
h
21
=
I
2
I
1
|
V
2
=
0
h
11
=
V
1
I
1
|
V
2
=
0
h
22
=
I
2
V
2
|
I
1
=
0
h
12
=
V
1
V
2
|
I
1
=
0
Doc 2
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Generator_(circuit_theory).html
[
V
1
I
2
]
=
[
h
11
h
12
h
21
h
22
]
[
I
1
V
2
]
Doc 3
0.5224
0.9134
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Electrical_element.html
[
V
1
I
2
]
=
[
0
n
-
n
0
]
[
I
1
V
2
]
[
V
1
V
2
]
=
[
0
-
r
r
0
]
[
I
1
I
2
]
Doc 4
0.5067
0.5067
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Port_(circuit_theory).html
[
V
1
V
2
]
=
[
z
11
z
12
z
21
z
22
]
[
I
1
I
2
]
Doc 5
0.3582
0.3582
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Mechanical_filter.html
[
V
F
]
=
[
z
11
z
12
z
21
z
22
]
[
I
v
]
Doc 6
0.2836
0.2836
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Impedance_analogy.html
[
v
F
]
=
[
z
11
z
12
z
21
z
22
]
[
i
u
]
Doc 7
0.2836
0.2836
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mobility_analogy.html
[
i
u
]
=
[
y
11
y
12
y
21
y
22
]
[
v
F
]
Doc 8
0.2601
0.3859
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Space-time_block_coding_based_transmit_diversity.html
[
x
1
x
2
*
]
=
[
h
1
-
h
2
h
2
*
h
1
*
]
[
S
1
S
2
*
]
+
[
n
1
n
2
*
]
[
S
^
1
S
^
2
*
]
=
[
h
1
-
h
2
h
2
*
h
1
*
]
-
1
[
x
1
x
2
*
]
=
1
h
1
h
1
*
+
h
2
h
2
*
[
h
1
*
h
2
-
h
2
*
h
1
]
[
x
1
x
2
*
]
Doc 9
0.2412
0.2412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Equivalent_impedance_transforms.html
[
V
1
0
]
=
[
R
1
+
R
2
-
R
2
-
R
2
R
2
+
R
3
]
[
I
1
I
2
]
Doc 10
0.2235
0.2235
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Axiomatic_design.html
[
F
R
1
F
R
2
]
=
[
A
11
A
12
A
21
A
22
]
[
D
P
1
D
P
2
]
Doc 11
0.1639
0.1639
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Block_matrix.html
𝐏
=
[
𝐏
11
𝐏
12
𝐏
21
𝐏
22
]
.
Doc 12
0.1638
0.1638
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Network_analysis_(electrical_circuits).html
[
V
1
V
0
]
=
[
z
(
j
ω
)
11
z
(
j
ω
)
12
z
(
j
ω
)
21
z
(
j
ω
)
22
]
[
I
1
I
0
]
Doc 13
0.1600
0.1600
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Impedance_parameters.html
(
V
1
V
2
)
=
(
Z
11
Z
12
Z
21
Z
22
)
(
I
1
I
2
)
Doc 14
0.1515
0.1515
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Belevitch's_theorem.html
𝐒
(
p
)
=
[
s
11
s
12
s
21
s
22
]
Doc 15
0.1449
0.1449
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Reduction_(mathematics).html
[
K
11
K
12
K
21
K
22
]
[
x
1
x
2
]
=
[
F
1
F
2
]
Doc 16
0.1416
0.2396
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Invariant_subspace.html
T
=
[
T
11
T
12
0
T
22
]
T
=
[
T
11
T
12
T
21
T
22
]
:
W
⊕
W
′
→
W
⊕
W
′
,
Doc 17
0.1399
0.1399
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Linear_independence.html
A
Λ
=
[
1
-
3
1
2
]
[
λ
1
λ
2
]
.
Doc 18
0.1333
0.1333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Admittance_parameters.html
(
I
1
I
2
)
=
(
Y
11
Y
12
Y
21
Y
22
)
(
V
1
V
2
)
Doc 19
0.1306
0.1306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/H-infinity_methods_in_control_theory.html
[
z
v
]
=
𝐏
(
s
)
[
w
u
]
=
[
P
11
(
s
)
P
12
(
s
)
P
21
(
s
)
P
22
(
s
)
]
[
w
u
]
Doc 20
0.1301
0.7930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Interior_reconstruction.html
[
f
1
g
1
]
=
[
A
B
C
D
]
[
0
y
0
]
[
f
g
]
=
[
A
B
C
D
]
[
x
y
]
[
f
g
]
=
[
A
B
C
D
]
[
x
y
]
.
[
x
y
]
=
[
A
B
C
D
]
-
1
[
f
g
]
[
x
1
y
1
]
=
[
A
B
C
D
]
-
1
[
f
-
f
1
g
e
x
]
[
x
0
y
0
]
=
[
A
B
C
D
]
-
1
[
f
g
e
x
]
[
x
1
y
1
]
=
[
A
B
C
D
]
-
1
[
f
g
1
+
g
1
e
x
]
Doc 21
0.1280
0.1280
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Haynsworth_inertia_additivity_formula.html
H
=
[
H
11
H
12
H
12
∗
H
22
]
Doc 22
0.1250
0.4621
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Local_inverse.html
[
f
g
]
=
[
A
B
C
D
]
[
x
y
]
[
f
g
]
=
[
A
B
C
D
]
[
x
y
]
[
x
0
y
0
]
=
[
E
F
G
H
]
[
f
g
]
[
x
1
y
1
]
=
[
E
F
G
H
]
[
f
-
B
y
0
g
-
D
y
0
]
Doc 23
0.1220
0.2709
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Mason's_invariant.html
[
Z
11
′
Z
12
′
Z
21
′
Z
22
′
]
=
[
Z
11
Z
12
Z
21
Z
22
]
-
1
[
Z
11
′
Z
12
′
Z
21
′
Z
22
′
]
=
[
n
11
n
12
n
21
n
22
]
[
Z
11
Z
12
Z
21
Z
22
]
[
n
11
n
12
n
21
n
22
]
[
Z
11
′
Z
12
′
Z
21
′
Z
22
′
]
=
[
Z
11
+
j
x
11
Z
12
+
j
x
12
Z
21
+
j
x
21
Z
22
+
j
x
22
]
Doc 24
0.1197
0.4318
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Transformation_matrix.html
[
x
′
y
′
]
=
[
1
0
k
1
]
[
x
y
]
[
x
′
y
′
]
=
[
1
k
0
1
]
[
x
y
]
[
x
′
y
′
]
=
[
cos
θ
-
sin
θ
sin
θ
cos
θ
]
[
x
y
]
[
x
′
y
′
]
=
[
cos
θ
sin
θ
-
sin
θ
cos
θ
]
[
x
y
]
Doc 25
0.1197
0.1197
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Composite_laminates.html
[
𝐍
𝐌
]
=
[
𝐀
𝐁
𝐁
𝐃
]
[
ε
0
κ
]
Doc 26
0.1157
0.4408
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Derivations_of_the_Lorentz_transformations.html
[
t
′
x
′
]
=
[
γ
δ
β
α
]
[
t
x
]
,
[
t
′
0
]
=
[
γ
δ
β
α
]
[
t
v
t
]
,
[
t
′
-
v
t
′
]
=
[
γ
δ
β
α
]
[
t
0
]
,
[
t
′
x
′
]
=
[
γ
δ
-
v
γ
γ
]
[
t
x
]
.
Doc 27
0.1121
0.4671
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Hyperelastic_material.html
W
=
W
(
I
1
,
I
2
)
W
=
W
(
I
¯
1
,
I
¯
2
)
W
=
W
(
I
1
)
W
=
W
(
I
1
)
W
(
s
y
m
b
o
l
F
)
=
W
^
(
I
1
,
I
2
)
Doc 28
0.1118
0.1118
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Stress_resultants.html
[
V
1
V
2
]
=
∫
-
t
/
2
t
/
2
[
σ
13
σ
23
]
d
x
3
.
Doc 29
0.1111
0.1111
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dynkin_diagram.html
A
=
[
2
a
12
a
21
2
]
Doc 30
0.1000
0.3875
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Antimetric_electrical_network.html
[
𝐒
]
=
[
S
11
S
12
S
12
S
11
]
[
𝐳
]
=
[
z
11
z
12
z
12
z
11
]
[
𝐒
]
=
[
S
11
S
12
S
12
-
S
11
]
[
𝐳
]
=
[
z
11
z
12
z
12
-
z
11
]
Doc 31
0.0990
0.0990
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Plane_stress.html
σ
i
j
=
[
σ
11
σ
12
σ
21
σ
22
]
≡
[
σ
x
τ
x
y
τ
y
x
σ
y
]
Doc 32
0.0972
0.0972
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Transmission_Loss_(duct_acoustics).html
[
p
^
i
q
^
i
]
=
[
A
B
C
D
]
[
p
^
o
q
^
o
]
Doc 33
0.0966
0.0966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/2D_computer_graphics.html
[
x
′
y
′
]
=
[
cos
θ
-
sin
θ
sin
θ
cos
θ
]
[
x
y
]
Doc 34
0.0966
0.0966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rotation_matrix.html
[
x
′
y
′
]
=
[
cos
θ
-
sin
θ
sin
θ
cos
θ
]
[
x
y
]
Doc 35
0.0966
0.0966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Rotation_(mathematics).html
[
x
′
y
′
]
=
[
cos
θ
-
sin
θ
sin
θ
cos
θ
]
[
x
y
]
Doc 36
0.0957
0.0957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Inverse-Wishart_distribution.html
𝐀
=
[
𝐀
11
𝐀
12
𝐀
21
𝐀
22
]
,
𝚿
=
[
𝚿
11
𝚿
12
𝚿
21
𝚿
22
]
Doc 37
0.0933
0.2533
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Scattering_parameters.html
(
b
1
b
2
)
=
(
S
11
S
12
S
21
S
22
)
(
a
1
a
2
)
(
b
1
a
1
)
=
(
T
11
T
12
T
21
T
22
)
(
a
2
b
2
)
(
a
1
b
1
)
=
(
T
11
T
12
T
21
T
22
)
(
b
2
a
2
)
Doc 38
0.0930
0.0930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/LU_decomposition.html
[
4
3
6
3
]
=
[
l
11
0
l
21
l
22
]
[
u
11
u
12
0
u
22
]
.
Doc 39
0.0915
0.0915
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Hyperbolic_equilibrium_point.html
[
x
n
+
1
y
n
+
1
]
=
[
1
1
1
2
]
[
x
n
y
n
]
modulo
1
Doc 40
0.0912
0.0912
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Homography_(computer_vision).html
p
a
=
[
x
a
y
a
1
]
,
p
b
′
=
[
w
′
x
b
w
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]
,
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a
b
=
[
h
11
h
12
h
13
h
21
h
22
h
23
h
31
h
32
h
33
]
Doc 41
0.0892
0.0892
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Spring_system.html
[
x
2
x
3
]
=
[
2
-
1
-
1
1
]
-
1
[
1
2
]
=
[
3
5
]
Doc 42
0.0851
0.0851
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Stretched_grid_method.html
I
2
=
λ
I
1
Doc 43
0.0848
0.0848
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Separation_principle.html
[
x
˙
e
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]
=
[
A
-
B
K
B
K
0
A
-
L
C
]
[
x
e
]
.
Doc 44
0.0845
0.0845
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Spinors_in_three_dimensions.html
X
=
2
[
ξ
1
ξ
2
]
[
-
ξ
2
ξ
1
]
.
Doc 45
0.0840
0.0840
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Sliding_mode_control.html
A
≜
[
a
11
A
12
A
21
A
22
]
Doc 46
0.0840
0.0840
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Neutral_particle_oscillation.html
M
=
(
M
11
M
12
M
21
M
22
)
Doc 47
0.0840
0.0840
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Surface_reconstruction.html
G
=
(
G
11
G
12
G
21
G
22
)
Doc 48
0.0828
0.1619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Cabibbo–Kobayashi–Maskawa_matrix.html
[
d
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s
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d
s
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,
[
d
′
s
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=
[
cos
θ
c
sin
θ
c
-
sin
θ
c
cos
θ
c
]
[
d
s
]
,
Doc 49
0.0819
0.0819
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Scale-invariant_feature_transform.html
[
u
v
]
=
[
m
1
m
2
m
3
m
4
]
[
x
y
]
+
[
t
x
t
y
]
Doc 50
0.0778
0.0778
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Beam_splitter.html
[
E
c
E
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[
r
a
c
t
b
c
t
a
d
r
b
d
]
[
E
a
E
b
]
,
Doc 51
0.0684
0.0684
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Common_integrals_in_quantum_field_theory.html
[
a
c
c
b
]
[
u
v
]
=
λ
[
u
v
]
.
Doc 52
0.0678
0.0678
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Weighted_arithmetic_mean.html
=
[
0.9901
0
0
0.9901
]
[
1
1
]
=
[
0.9901
0.9901
]
Doc 53
0.0652
0.0652
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Wagner_model.html
h
(
I
1
,
I
2
)
Doc 54
0.0625
0.0625
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Herbert_Scarf.html
h
=
(
h
1
,
h
2
,
⋯
,
h
n
)
Doc 55
0.0559
0.0559
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Dehn–Sommerville_equations.html
h
(
P
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=
(
h
0
,
h
1
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,
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d
)
Doc 56
0.0559
0.0559
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/H-vector.html
h
(
Δ
)
=
(
h
0
,
h
1
,
…
,
h
d
)
Doc 57
0.0504
0.0504
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Differential_geometry_of_curves.html
[
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κ
(
t
)
0
]
[
𝐞
1
(
t
)
𝐞
2
(
t
)
]
Doc 58
0.0485
0.0485
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Hückel_method.html
[
H
11
-
E
S
11
H
12
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E
S
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21
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E
S
21
H
22
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E
S
22
]
×
[
c
1
c
2
]
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0
Doc 59
0.0294
0.0294
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Simplicial_complex.html
(
h
0
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h
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.