Feasible

Motion-Planning Algorithm

Optimal

Trajectory

Inner Product Space

Inner Product

Orthogonal Complement

Orthogonal

Orthonormal

Affine

Bijective

Composition

Identity Map

Image

Invertibility

Kernel

Linear Map

Linear Operator

Preimage

Set of Linear Maps

Adjoint

Diagonal

Diagonalizable

Matrix of Linear Map

Orthogonal Matrix

Orthonormal Matrix

Positive Definite

Positive Semidefinite

Rank

Singular

Trace

Upper-Triangular

Complementary Subspaces

Direct Sum

Finite Basis

Finite Dimensional

Invariant Subspace

Invariant

Linear Combination

Linear Independence

Orthogonal Vector

Span

Subspace

Vector Space

Determinants for Linearly Transformed Autocorrelation Matrices

Finite Variance = Autocorrelation symmetric + positive semidefinite

Linear Transform for Autocorrelation Matrices

Distinct eigenvalues have linearly independent eigenvectors

Eigendecomposition of a Matrix

Existence of Eigenvalues on Complex Spaces

Positive Definite = Positive Eigenvalues

Positive Semidefinite has dim Eigenvectors

Trace and Determinant with Eigenvalues

Dimensionality & Linear Maps

Injectivity, surjectivity, and isomorphism are equivalent when Dimension is the Same

Inverse to a Linear Map is Unique

Isomorphism is a Bijection

Linear maps are defined on a basis

Properties of Linear Maps

Norm-Preserving Matrix

Orthogonal Matrices have Determinant 1

Isomorphic Vector Spaces have the Same Dimension

1-Norm

2-Norm

Norm

Operator Norm

Borel function

Borel space

Borel subset

Borel σ-algebra

Fσ set

Gδ set

σ-algebra containing all Borel subsets

Limit of Measurable Functions is Measurable

Measurability Criterion for Topological Codomain

Supremum & Infimum Preserve Measurability

Concave Function

Conjugate Exponents

Convex Set

Convex

Convexity implies continuity

Hölder's Inequality

Jensen's Inequality

Minkowski's Inequality

Borel measure

Concentrated

Law

Lebesgue-Stieltjes Integral

Lebesgue-Stieltjes Measure

Mutually Singular

Radon-Nikodym Derivative

Variation

h-interval

Equivalence between Density and Radon-Nikodym Derivative

Radon-Nikodym Theorem

Change of Variable Formula

Lebesgue Integral is a Measure

Essential bound

Infinity Norm

Integrable

L infinity

Lp Convergence

Lp Norm

Lp Space

Set of all Integrable Functions

Uniform Integrability

Absolute Continuity of Lebesgue Integral

Continuous and Compactly supported functions dense in Lp

Integrable = Vector Space

Integrals of Functions that are Zero a.e.

Lebesgue Integral Triangle Inequality

Lp is Banach

S is dense in Lp

Darboux Sums

Mesh

Riemann Integral

Riemann-Stieltjes Integral

Riemann integral existence

Continuous

Lipschitz Continuous

Right Continuous

Semicontinuous

Convergence

Pointwise Convergence

Controllability Gramian

Controllability Matrix

Controllable

Driftless Control System

Observability Gramian

Observability Matrix

Observability Problem

Observable

Affine Control System

Barrier Certificate

Class Κ

Control Barrier Function

Forward Invariant

Invariant Set

Safe Set

Polish space

Weak convergence

Bounded-Lipschitz

Total Variation

Measurable Selection Conditions

Bellman's Optimality Principle

Blackwell's Irrelevant Information Theorem

Discounted Cost

Policy Relationships

Value Iteration Algorithm

Q-Learning

Optimality of Q Learning Algorithm

Dynamic

Sequential

Static

Stationary Team Policy

Strictly Causal

Time Consistent

Quadratic Gaussian Team

Standard Quadratic Team

Static Quadratic Team

Nash Equilibrium

Team-Optimal Solution

Properties of LGQT Cost

Existence for N-agent Team

Stationary Conditions for Team Optimality

Uniqueness for N-agent Team

Conditions for PBP Optimality to be Global

Radner Krainak Theorem

Stationary Radner Krainak Theorem

Kac's Lemma (Stationary Ergodic)

Lempel-Ziv Coding

Prefix Code

Shannon-Fano-Elias Code

Achievable (Continuous)

Average Cost Constraint

Average Power Constraint

Block Codes for the Gaussian Channel

Continuous Memoryless Source

Differential Cross-Entropy

Differential Divergence

Differential Entropy

Discrete-Time Continuous Memoryless Channels

Discrete-Time Memoryless Gaussian Channel (AWGN Channel)

Fading Channel

Information Capacity with Input Cost

Multivariate Gaussian

Operational Channel Capacity (Continuous)

Typical Set

Volume

AEP For Continuous IID RVs

Capacity of Correlated Parallel Gaussian Channels

Capacity of Uncorrelated Parallel Gaussian Channels

Capacity with Decoder-Side Information (DSI)

Capacity with Full-Side Information (FSI)

Concavity of Channel Capacity in P

Consequence of the AEP

Equivalent Properties in Discrete & Continuous IT

Estimation Error and differential entropy

Gaussian Noise Minimizes Capacity of Additive-Noise Channel

Joint Differential Entropy of Multivariate Gaussian

Shannon's Channel Coding Theorem for AWGN

Uniform Quantization of Real-Valued Source

Upper Bound on Channel Capacity

Cross-Entropy

Discrete Memoryless Source

Divergence

Entropy Rate

Entropy

Ergodic

Jensen-Shannon Divergence

Joint Entropy

Mutual Information

Renyi Divergence

Renyi Entropy

Self-Information

Source Entropy

Source

State

Stationary & Ergodic Source

Stationary Distribution

Stationary

Typical Set

Asymptotic Equipartition Property

Cesaro-Mean Theorem

Convexity or Concavity of Information Measure

Data Processing Inequality

Fundamental Inequality

Kraft Inequality

Log-Sum Inequality

Almost Sure Convergence

Convergence in Distribution

Convergence in Expectation

In Probability Convergence

Norm-like Function

Pointwise Convergence

Central Limit Theorem

Existence of Sequences of Independent rvs

Law of Large Numbers

Portmanteau's Theorem

Prokhorov's Theorem

Scheffé's Theorem

Skohorod's Theorem

Theorems on Convergence

Conditional Expectation

Conditional Variance

Covariance Matrix

Covariance

Expectation

Moment

Orthogonal

Probability Measure

Variance

Cauchy-Schwartz Inequality

Chebyshev Inequality

Expectation of a Function of a Random Variable

Jensen's Inequality

Markov's Inequality

Almost surely

Bernoulli Trial

Coin Tossing Probability Space

Conditional Probability of Events

Decreasing Events

Distribution

Event Space

Exchangeable

Increasing Events

Independent

Limits of Events

Probability Space

Random Variable

Random Vector

Relatively Sequentially Compact

Sample Space

Tail Field

Tight

iid

σ(X)

Axioms of Probability

Bayes' Rule

Borel-Cantelli Lemma

Continuity of Probability

Countable Sub-additivity of Events

De Finetti's Theorem

Existence of Uniform Measure

Extension Theorem

Kolmogorov 0-1 Law

Law of Total Probability

Inversion Method

Memoryless Property 1

(A) Ring Generated by R

(P) Predictable σ-algebra

(R) Set of Predictable Rectangles

(Ɛ) Simple Predicable Processes

(Λ) Set of Predictable Locally Integrable Processes

Doléans Measure

Itô Isometry

Itô Stochastic Integral

Mutual Variation

Semimartingale Integral

Semimartingale

Stochastic Interval

Bichteler-Dellacherie Theorem

Cross Variation

Density of Ɛ

Independence of Bounded RV

Itô Isometry v2

Itô Isometry v3

Itô Representation Theorem

Itô Stochastic Integral is a Local Martingale

Itô Stochastic Integral on Ɛ is a R.C. Martingale

Itô Stochastic Integral on Λ is a R.C. Martingale

Itô's Formula

Left Continuous Adapted = Predictable

Multidimensional Itô Formula

Mutual Variation of Itô Stochastic Integrals

Predictable Stochastic Intervals

Quadratic Variation is CAII

Quadratic Variation

Semimartingale Properties

Solution to SDE

Stopping Time Integral

Admissible

Asian Call Option

Derivative

European Call Option

European Put Option

Forward Contract

Market Model

Portfolio

Replicating Portfolio

Self-Financing

No Arbitrage

Brownian Motion

Dirac Distribution

Gaussian Process

Jump Chain

Poisson Process

Excursion Time

Hitting Time

Holding Time

Jump Time

Occupation Time

Passage Time

Random Time

Stopping Time