Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

EMCH 799 > Math > Flashcards

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

ASAP

A

Adjoint Sensitivity Analysis Procedure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

BLUE

A

Best Linear Unbiased Estimator

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

CDF

A

Cumulative Distribution Function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

CG

A

Conjugate-gradient

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

CONMIN

A

Conjugate-minimization

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

DASAP

A

Discrete Adjoint Sensitivity Analysis Procedure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

DASE

A

Discrete Adjoint Sensitivity Equations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

DDR

A

Discrete Response Sensitivity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

DFSAP

A

Discrete Forward Sensitivity Analysis Procedure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

DFSE

A

Discretized Forward Sensitivity Analysis Procedure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

FAST

A

Fourier Amplitude Sensitivity Test

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

FFT

A

Fast Fourier Transform

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

FSAP

A

Forward Sensitivity Analysis Procedure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

FSE

A

Forward Sensitivity Equations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

HOT

A

Higher-Order-Term

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

LMQN

A

Limited-Memory Quasi-Newton

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

ME

A

Model Error

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

MGF

A

Moment Generating Function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

MLE

A

Maximum Likelihood Estimator

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

OI

A

Optimal Interpolation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

PDE

A

Partial Differential Equation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

PDF

A

Probability Density Function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

PSAS

A

Physical Space Statistical Analysis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

QN

A

Quasi-Newton

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

SOR

A

Successive Over Relaxation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

SQP

A

Sequential Quadratic Programming

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

SVD

A

Singular Value Decomposition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

SWE

A

Shallow Water Equations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

T-N

A

Truncated Newton

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

VDA

A

Variational Data Assimilation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

IFF

A

If and Only If

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

3-D VAR

A

Three-Dimensional Variational Data Assimilation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

4-D VAR

A

Four-Dimensional Variational Data Assimilation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

Normal Linear Operator

A

A linear operator “A” is called normal if it commutes with its adjoint: AA^+ = A^+A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

Hermitian Linear Operator

A

A linear operator “H” is called hermitian if it is equal to its adjoint: H^+ = H

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

Unitary Linear Operator

A

A linear operator “U” is called unitary if it is inverse to its adjoint: UU^+ = I

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

δik

A

Kronecker symbol

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

Identifiability

A

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.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

Homeomorphism

A

An instance of topological equivalence to another space or figure

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

Concatenate

A

link (things) together in a chain or series

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

EKF

A

Extended Kalman Filter

43
Q

TV

A

Total Variation

44
Q

Blocky Profile

A

“Blocky Profile” refers to functions that are piecewise constant and hence have sharply defined edges.

45
Q

GLB

A

Greatest lower bound

46
Q

Number Field “F”

A

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
Q

Null (Zero) Vector

A

the vector with all components zero

48
Q

Scalar

A

a real vector having just one component

49
Q

Linear Vector Space “V”

A

a set or a collection, V, of real vectors of size m is called a (linear) vector space

50
Q

Neighborhood

A

A neighborhood of a point is any set that contains an open set that itself contains the point

51
Q

Inner Product

A

denoted . Must be positive definite, commutative, additive, and homogeneous.

52
Q

Norm of a vector x

A

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
Q

Normed Vector Space

A

A vector space “V” endowed with a norm

54
Q

FLOP

A

Floating Point Operations

55
Q

Orthogonality

A

Two vectors x and y are called orthogonal if their inner product is zero

56
Q

Span

A

denotes the set of all linear combination of vectors in S

57
Q

Basis

A

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
Q

Dim(V)

A

Dimension of V

59
Q

Parseval’s Identity

A

Parseval’s identity indicates that the total energy in any representation remains unchanged when “S” is a complete orthonormal basis.

60
Q

Rectangular Matrix

A

A rectangular array of numbers of the field “F,” composed of m rows and n columns.

61
Q

Null (Zero) Matrix

A

Contains all elements as 0

62
Q

Principal (Main) Diagonal of A

A

The set of elements (a11, a22,…,amm)

63
Q

Super Diagonals

A

Diagonals parallel to the principal diagonal and above

64
Q

Sub Diagonals

A

Diagonals parallel to the principal diagonal and below

65
Q

Column Matrix

A

a rectangular matrix consisting of a single column

66
Q

Row Matrix

A

A rectangular matrix consisting of a single row

67
Q

Diagonal Matrix

A

A square matrix with zero off-diagonal elements

68
Q

Unit (Identity) Matrix

A

A diagonal matrix with aii=1, for all i.

69
Q

Symmetrix Matrix

A

A square matrix “S” that coincides with its transpose

70
Q

Skew-symmetric Matrix

A

A matrix with elements aij=-aji, for all i,j.

71
Q

Hermitian Matrix

A

A matrix with elements aij=aji(bar), for all i,j; here, the overbear denotes complex conjugation.

72
Q

Basic Operations on Matricies

A
  1. Addition (Summation)
  2. Scalar multiplication of a matrix by a number
  3. Multiplication of matrices
73
Q

nilpotent

A

A square matrix “A” is called nilpotent iff there is an integer “p” such that A^p=0.

74
Q

detA

A

Determinant of “A” or IAI

75
Q

Rank(A)

A

Rank of a matrix “A.” The number of linearly independent column (rows) of “A” is called the column (row) rank of “A.”

76
Q

Singular Matrix

A

detA=0

77
Q

tr(A)

A

The trace of “A” is a scalar defined by the sum of the diagonal elements of “A”

78
Q

R(A)

A

Range space of “A”

79
Q

N(A)

A

Null Space of “A”

80
Q

Reflexivity

A

A matrix “A” is always similar to itself

81
Q

Symmetry

A

If A”A is similar to “B,” then “B” is similar to “A”

82
Q

Transitivity

A

If “A” is similar to “B,” and “B” is similar to “C,” then “A” is similar to “C.”

83
Q

Orthogonal Matrix

A

if Q^-1=Q^T

84
Q

Is a permutation matrix singular or non-singular?

A

non-singular

85
Q

Is the identity matrix a permutation matrix?

A

yes

86
Q

Are permutation matrices orthogonal?

A

yes

87
Q

Are Grammian matrices symmetric?

A

yes

88
Q

Define the Spectrum of “A”

A

The set of all eigenvalues of “A”

89
Q

Define “Spectra Radius”

A

The magnitude of the largest eigenvalue

90
Q

rho(A)

A

spectral radius

91
Q

characteristic vector, proper vector, latent vector

A

eigenvector

92
Q

characteristic value, proper value, latent value, latent root, latent number, characteristic number

A

eigenvalue

93
Q

Define MGF

A

the expectation of e^(tx)

94
Q

The ___ distribution is widely used in radioactivity applications and in equipment failure rate analysis.

A

The exponential distribution

95
Q

The ___ distribution is often used for weighting probabilities along the unit interval.

A

The beta distribution

96
Q

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.

A

The log-normal distribution

97
Q

Krylov Subspace

A

Krylov subspaces are intimately related to matrix-polynomials, and are important in reduced-space computations and error estimation.

98
Q

II”A”II denotes

A

Norm of a square matrix “A”

99
Q

Banach Space

A

A complete normed vector space, V

100
Q

pre-Hilbert Space

A

A space, “V,” equipped with an inner product

101
Q

Hilbert Space

A

A pre-Hilbert space that is complete WRT the norm. Usually denoted “H”

102
Q

nondegenerate

A

A sequence of vectors x1, x2,… is called non degenerate if, for every p, the vectors x1, x2,…,xp are linearly independent.

103
Q

Orthogonal

A

A sequence of vectors is called orthogonal if any two vectors of the sequence are orthogonal.

104
Q

Orthogonalization

A

Orthogonalization of a sequence of vectors is the process of replacing the sequence boy an equivalent orthogonal sequence.

EMCH 799 (7 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions