Shadow was a graphical user interface (GUI) for the OS/2 operating system, primarily developed during the early 1990s. It was designed as a desktop environment that provided users with a more visually appealing and user-friendly experience than the standard OS/2 GUI at the time. Shadow aimed to enhance user interaction by offering features such as improved window management, customizable desktop elements, and better integration of applications.

TOPS can refer to various things depending on the context. Here are a few common interpretations: 1. **TOPS (Tera Operations Per Second)**: In computing, this term is used to measure the performance of artificial intelligence and high-performance computing systems. It refers to the number of trillion operations a system can perform in one second.

An accumulation point (or limit point) of a subset \( A \) of a topological space \( X \) is a point \( x \in X \) such that every neighborhood of \( x \) contains at least one point from \( A \) that is different from \( x \) itself.

Heiligenschein, which translates to "holy light" in German, refers to an optical phenomenon that occurs when a light source, such as the sun, shines on dewdrops or mist with a dark background. This effect creates a bright halo or light ring around the shadow of an object, usually seen in nature. The phenomenon is due to the interaction of light with the spherical shape of the water droplets, which acts like tiny lenses.

A **periodic point** is a concept from dynamical systems and mathematical analysis. Specifically, a point \( x \) in a dynamical system is said to be periodic with period \( n \) if, when the system iteratively applies a function \( f \), the point eventually returns to its original position after \( n \) iterations.

Invariant subspaces are a concept from functional analysis and operator theory that refers to certain types of subspaces of a vector space that remain unchanged under the action of a linear operator. More specifically: Let \( V \) be a vector space and \( T: V \to V \) be a linear operator (which can be a matrix in finite dimensions or more generally a bounded or unbounded linear operator in infinite dimensions).

Richard M. Friedberg is a prominent figure in the field of mathematics, particularly known for his work in mathematical education and research. He is often associated with topics related to mathematical logic, algebra, and mathematical theory. If you have a more specific context or aspect of Richard M.

Orthonormality is a concept found primarily in linear algebra and functional analysis, particularly in the context of vector spaces and inner product spaces. A set of vectors is said to be orthonormal if the following two conditions are satisfied: 1. **Orthogonality**: The vectors are orthogonal to each other, meaning that the inner product (dot product in Euclidean space) of any two distinct vectors is zero.

A basis function is a fundamental component in various fields such as mathematics, statistics, and machine learning. It serves as a building block for constructing more complex functions or representations. Here are some key points about basis functions: 1. **Mathematical Definition**: In the context of functional analysis, a set of functions is considered a basis if any function in a certain function space can be expressed as a linear combination of those basis functions.

In the context of module theory, which is a branch of abstract algebra, the direct sum of modules is a way to combine two or more modules into a new module.

The characteristic polynomial is a polynomial that is derived from a square matrix and is used in linear algebra to provide important information about the matrix, particularly its eigenvalues.

A glossary of linear algebra typically includes key terms and concepts that are fundamental to the study and application of linear algebra. Here’s a list of some important terms you might find in such a glossary: ### Glossary of Linear Algebra 1. **Vector**: An element of a vector space; often represented as a column or row of numbers. 2. **Matrix**: A rectangular array of numbers arranged in rows and columns.

A **controlled invariant subspace** is a concept from control theory and linear algebra that pertains to the behavior of dynamical systems. In the context of linear systems, it often refers to subspaces of the state space that are invariant under the action of the system's dynamics when a control input is applied.

A **convex cone** is a fundamental concept in mathematics, particularly in linear algebra and convex analysis.

In linear algebra and functional analysis, the concept of a dual basis is tied to the idea of dual spaces.

Eigenplane is a technique related to the fields of machine learning and computer vision that typically involves dimensionality reduction and representation learning. It is often used to represent complex data by finding a lower-dimensional space that captures the essential features of the data while retaining its important characteristics.

A finite von Neumann algebra is a special type of von Neumann algebra that satisfies certain properties related to its structure and its trace. Von Neumann algebras are a class of *-algebras of bounded operators on a Hilbert space that are closed in the weak operator topology. They play a central role in functional analysis and quantum mechanics.

In linear algebra, a **frame** is a concept that generalizes the idea of a basis in a vector space. While a basis is a set of linearly independent vectors that spans the vector space, a frame can include vectors that are not necessarily independent and may provide redundancy. This redundancy is beneficial in various applications, particularly in signal processing and data analysis.

Loewner order, named after the mathematician Charles Loewner, is a way to compare positive definite matrices. In particular, for two symmetric matrices \( A \) and \( B \), we say that \( A \) is less than or equal to \( B \) in the Loewner order, denoted \( A \preceq B \), if the matrix \( B - A \) is positive semidefinite.

The joint spectral radius is a concept from the field of dynamical systems and control theory that deals with the long-term behavior of sets of matrices. It is particularly relevant in the study of systems that can be described by multiple linear transformations, typically when analyzing the stability and robustness of systems involving several processes or state transitions.