"A Little Bit of Country" could refer to a few different things, depending on the context: 1. **Music or Songs**: It might be the title of a country music song or album by an artist. Country music often explores themes related to rural life, love, and personal experiences. 2. **Television or Movies**: It could refer to a film, TV show, or documentary that focuses on country life or culture.

"All Out & Down" is a term that can refer to various contexts depending on how it's used, but it does not have a widely recognized or specific definition in popular culture or other fields as of my last knowledge update in October 2023. It could imply a total commitment to a cause or activity and experiencing a downturn in some way, but without additional context, it's difficult to provide a precise meaning.

"Allting som ni gör kan jag göra bättre" is a Swedish phrase that translates to "Everything you do, I can do better" in English. This phrase is often associated with themes of competition or confidence in one's own abilities.

"Après" is a French word that means "after." It is often used in various contexts, particularly in phrases like "après-ski," which refers to social activities and entertainment that take place after skiing or snowboarding. In this context, it can include gatherings, parties, or relaxation in ski resorts. In a broader sense, "après" can be used in different contexts in the culinary world, lifestyle, or as an expression of relaxation and enjoyment following an activity.

"Animetal Marathon II" is a musical album by the Japanese band Animetal, known for their heavy metal covers of popular anime theme songs and soundtracks. This album is part of a series in which the band performs energetic, metal versions of iconic anime music. Animetal is celebrated for blending the world of anime and heavy metal, appealing to fans of both genres.

"Another Side" is an album by British singer and performer John Barrowman, released in 2010. It features a mix of musical styles, showcasing Barrowman's versatile vocal abilities. The album includes a selection of songs that reflect Barrowman's theatrical background, incorporating both contemporary pop and classic show tunes. Notable tracks often highlight his strengths in emotive vocal performances and engaging interpretations.

"Another Time, Another Place" is the second studio album by British singer-songwriter Bryan Ferry, released in 1974. This album features a mix of original songs penned by Ferry and covers of popular tracks from other artists. Known for its distinctive blend of glam rock and art rock, "Another Time, Another Place" showcases Ferry's smooth vocal style and sophisticated songwriting. The album includes popular tracks like "The 'In' Crowd" and "Smoke Gets in Your Eyes.

"Classics II" can refer to several different things depending on the context. Here are a few possibilities: 1. **Music**: It may refer to a collection of classical music pieces or a specific album that features orchestral works or instrumental performances from renowned composers. 2. **Video Games**: "Classics II" could refer to a sequel or a compilation of classic video games, often remastered or re-released for modern consoles.

Cover Two, often referred to as "Tampa Two," is a defensive scheme used in American football, primarily in the secondary. In this coverage, the defense divides the field into two deep zones, with two safeties responsible for the deep halves of the field.

"Bande à Part" is a studio album by the French rock band Nouvelle Vague, released in 2006. The album features a collection of covers of well-known songs from various genres, reinterpreted in the band's unique bossa nova and lounge style. The title, which translates to "A Gang Apart," references the 1964 film of the same name directed by Jean-Luc Godard.

Every vector space is defined over a field.

E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, the real numbers. And in ${\mathbb{C}}^2$ the underlying field is $\mathbb{C}$, the complex numbers.

Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.

Elements of the underlying field of a vector space are known as scalar.

A member of the underlying field of a vector space. E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, and a scalar is a member of $\mathbb{R}$, i.e. a real number.

A linear map $A$ can be seen as a (1,1) tensor because:is a number, $v\ast$. is a dual vector, and W is a vector. Furthermoe, $T$ is linear in both $v\ast$ and $w$. All of this makes $T$ fullfill the definition of a (1,1) tensor.

Bibliography:

$T^{(m,n)}$ has order $(m,n)$

TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.

Vectors with the index on top such as $x^i$ are the "regular vectors", they are called covariant vectors.

Those in indices on bottom are called contravariant vectors.

It is possible to change between them by Raising and lowering indices.

The values are different only when the metric signature matrix is different from the identity matrix.