The fear of being embarrassed due to lack of sportsmanship is known as "athazagoraphobia." This fear can stem from a variety of sources, such as a fear of being judged by others, a fear of losing respect or credibility, or a fear of disappointing oneself or others. It can lead individuals to feel anxious or self-conscious in competitive or team sports settings, and may impact their ability to fully engage in the game or activity. Overcoming this fear may involve building confidence, practicing good sportsmanship, and focusing on personal growth rather than external validation. **

The relationship between the variables is non-linear. **

A linear extension with respect to a relation is a total ordering of the elements in the domain of the relation that preserves the original ordering of the elements in the relation. In other words, it is a way of arranging the elements in the domain such that the original ordering of the elements in the relation is maintained. Linear extensions are often used in the context of partially ordered sets and can help to provide a linear ordering of the elements in the set. **

"Equality before, but justice first" suggests that while equality is important, it should not come at the expense of justice. This phrase emphasizes the need to address systemic injustices and inequalities in order to achieve true equality. It implies that simply treating everyone the same does not necessarily address the underlying issues of discrimination and oppression. Instead, it calls for prioritizing justice in order to create a more equitable society for all. **

A linear term is a single variable or constant raised to the power of 1, such as 3x or 5. A linear equation is an equation that can be written in the form y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope, and b is the y-intercept. A linear function is a mathematical relationship between two variables that can be represented by a straight line on a graph, and it can be expressed in the form f(x) = mx + b, where f(x) represents the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. **

The linear span of a linear space is the set of all possible linear combinations of the vectors in that space. In other words, it is the collection of all possible vectors that can be obtained by scaling and adding the vectors in the space. The linear span forms a subspace of the original space and is often used to describe the "space" that is covered by the original set of vectors. It is a fundamental concept in linear algebra and is used to understand the properties and structure of vector spaces. **

Linear algebra is the branch of mathematics that deals with vector spaces and linear transformations. Linear mappings are a fundamental concept in linear algebra, as they represent transformations that preserve the structure of vector spaces. Linear algebra provides the tools and techniques to study and analyze linear mappings, such as matrix representations, eigenvalues, and eigenvectors. Understanding linear algebra is essential for understanding the properties and behavior of linear mappings in various mathematical contexts. **

Linear algebra is the branch of mathematics that deals with vector spaces and linear equations. Linear transformations are functions that preserve vector addition and scalar multiplication, which are fundamental concepts in linear algebra. Linear transformations can be represented by matrices, and studying linear algebra helps us understand the properties and behavior of linear transformations. In essence, linear algebra provides the tools and framework to analyze and manipulate linear transformations. **