Math Flashcards
1
Q
Infimum
A
the infimum (plural infima) of a subset S of a partially ordered set T is the greatest element of T that is less than or equal to all elements of S. Consequently the term greatest lower bound (abbreviated as GLB) is also commonly used.
2
Q
ASAP
A
Adjoint Sensitivity Analysis Procedure
3
Q
BLUE
A
Best Linear Unbiased Estimator
4
Q
CDF
A
Cumulative Distribution Function
5
Q
CG
A
Conjugate-gradient
6
Q
CONMIN
A
Conjugate-minimization
7
Q
DASAP
A
Discrete Adjoint Sensitivity Analysis Procedure
8
Q
DASE
A
Discrete Adjoint Sensitivity Equations
9
Q
DDR
A
Discrete Response Sensitivity
10
Q
DFSAP
A
Discrete Forward Sensitivity Analysis Procedure
11
Q
DFSE
A
Discretized Forward Sensitivity Analysis Procedure
12
Q
FAST
A
Fourier Amplitude Sensitivity Test
13
Q
FFT
A
Fast Fourier Transform
14
Q
FSAP
A
Forward Sensitivity Analysis Procedure
15
Q
FSE
A
Forward Sensitivity Equations
16
Q
HOT
A
Higher-Order-Term
17
Q
LMQN
A
Limited-Memory Quasi-Newton
18
Q
ME
A
Model Error
19
Q
MGF
A
Moment Generating Function
20
Q
MLE
A
Maximum Likelihood Estimator
21
Q
OI
A
Optimal Interpolation
22
Q
PDE
A
Partial Differential Equation
23
Q
A
Probability Density Function
24
Q
PSAS
A
Physical Space Statistical Analysis
25
QN
Quasi-Newton
26
SOR
Successive Over Relaxation
27
SQP
Sequential Quadratic Programming
28
SVD
Singular Value Decomposition
29
SWE
Shallow Water Equations
30
T-N
Truncated Newton
31
VDA
Variational Data Assimilation
32
IFF
If and Only If
33
3-D VAR
Three-Dimensional Variational Data Assimilation
34
4-D VAR
Four-Dimensional Variational Data Assimilation
35
Normal Linear Operator
A linear operator "A" is called normal if it commutes with its adjoint: AA^+ = A^+A
36
Hermitian Linear Operator
A linear operator "H" is called hermitian if it is equal to its adjoint: H^+ = H
37
Unitary Linear Operator
A linear operator "U" is called unitary if it is inverse to its adjoint: UU^+ = I
38
δik
Kronecker symbol
39
Identifiability
An unknown parameter is "identifiable" if it can be determined uniquely in all points of its domain by using the input-output relation of the system and the input-output data.
40
Homeomorphism
An instance of topological equivalence to another space or figure
41
Concatenate
link (things) together in a chain or series
42
EKF
Extended Kalman Filter
43
TV
Total Variation
44
Blocky Profile
"Blocky Profile" refers to functions that are piecewise constant and hence have sharply defined edges.
45
GLB
Greatest lower bound
46
Number Field "F"
An arbitrary collection of numbers within which the four operations of addition, subtraction, multiplication, and division by a nonzero number can always be carried out.
47
Null (Zero) Vector
the vector with all components zero
48
Scalar
a real vector having just one component
49
Linear Vector Space "V"
a set or a collection, V, of real vectors of size m is called a (linear) vector space
50
Neighborhood
A neighborhood of a point is any set that contains an open set that itself contains the point
51
Inner Product
denoted . Must be positive definite, commutative, additive, and homogeneous.
52
Norm of a vector x
IIxII, is a nonnegative real scalar that indicates the size or the length of the vector x, and is positive definite, homogeneous, and triangle inequality
53
Normed Vector Space
A vector space "V" endowed with a norm
54
FLOP
Floating Point Operations
55
Orthogonality
Two vectors x and y are called orthogonal if their inner product is zero
56
Span
denotes the set of all linear combination of vectors in S
57
Basis
If every vector in "V" can be uniquely expressed as a linear combination of those in S, then S is called a basis for V.
58
Dim(V)
Dimension of V
59
Parseval's Identity
Parseval's identity indicates that the total energy in any representation remains unchanged when "S" is a complete orthonormal basis.
60
Rectangular Matrix
A rectangular array of numbers of the field "F," composed of m rows and n columns.
61
Null (Zero) Matrix
Contains all elements as 0
62
Principal (Main) Diagonal of A
The set of elements (a11, a22,...,amm)
63
Super Diagonals
Diagonals parallel to the principal diagonal and above
64
Sub Diagonals
Diagonals parallel to the principal diagonal and below
65
Column Matrix
a rectangular matrix consisting of a single column
66
Row Matrix
A rectangular matrix consisting of a single row
67
Diagonal Matrix
A square matrix with zero off-diagonal elements
68
Unit (Identity) Matrix
A diagonal matrix with aii=1, for all i.
69
Symmetrix Matrix
A square matrix "S" that coincides with its transpose
70
Skew-symmetric Matrix
A matrix with elements aij=-aji, for all i,j.
71
Hermitian Matrix
A matrix with elements aij=aji(bar), for all i,j; here, the overbear denotes complex conjugation.
72
Basic Operations on Matricies
1. Addition (Summation)
2. Scalar multiplication of a matrix by a number
3. Multiplication of matrices
73
nilpotent
A square matrix "A" is called nilpotent iff there is an integer "p" such that A^p=0.
74
detA
Determinant of "A" or IAI
75
Rank(A)
Rank of a matrix "A." The number of linearly independent column (rows) of "A" is called the column (row) rank of "A."
76
Singular Matrix
detA=0
77
tr(A)
The trace of "A" is a scalar defined by the sum of the diagonal elements of "A"
78
R(A)
Range space of "A"
79
N(A)
Null Space of "A"
80
Reflexivity
A matrix "A" is always similar to itself
81
Symmetry
If A"A is similar to "B," then "B" is similar to "A"
82
Transitivity
If "A" is similar to "B," and "B" is similar to "C," then "A" is similar to "C."
83
Orthogonal Matrix
if Q^-1=Q^T
84
Is a permutation matrix singular or non-singular?
non-singular
85
Is the identity matrix a permutation matrix?
yes
86
Are permutation matrices orthogonal?
yes
87
Are Grammian matrices symmetric?
yes
88
Define the Spectrum of "A"
The set of all eigenvalues of "A"
89
Define "Spectra Radius"
The magnitude of the largest eigenvalue
90
rho(A)
spectral radius
91
characteristic vector, proper vector, latent vector
eigenvector
92
characteristic value, proper value, latent value, latent root, latent number, characteristic number
eigenvalue
93
Define MGF
the expectation of e^(tx)
94
The ___ distribution is widely used in radioactivity applications and in equipment failure rate analysis.
The exponential distribution
95
The ___ distribution is often used for weighting probabilities along the unit interval.
The beta distribution
96
The ___ distribution is particularly useful for modeling nonnegative phenomena, such as analysis of incomes, classroom sizes, masses or sizes of biological organisms, evaluation of neutron cross sections, scattering of subatomic particles, etc.
The log-normal distribution
97
Krylov Subspace
Krylov subspaces are intimately related to matrix-polynomials, and are important in reduced-space computations and error estimation.
98
II"A"II denotes
Norm of a square matrix "A"
99
Banach Space
A complete normed vector space, V
100
pre-Hilbert Space
A space, "V," equipped with an inner product
101
Hilbert Space
A pre-Hilbert space that is complete WRT the norm. Usually denoted "H"
102
nondegenerate
A sequence of vectors x1, x2,... is called non degenerate if, for every p, the vectors x1, x2,...,xp are linearly independent.
103
Orthogonal
A sequence of vectors is called orthogonal if any two vectors of the sequence are orthogonal.
104
Orthogonalization
Orthogonalization of a sequence of vectors is the process of replacing the sequence boy an equivalent orthogonal sequence.
