Not to be confused with algebra over a field, which is a particular algebraic structure studied within algebra.

The definition implies that this is also a symmetric matrix.

The Wikipedia page of this article is basically a masterclass why Wikipedia is useless for learning technical subjects. They are not even able to teach such a simple subject properly there!

Bibliography:

William Morris Kinnersley (1860-1928) was an American architect known for his work in the late 19th and early 20th centuries. He was active primarily in the Pacific Northwest and is recognized for his contributions to various architectural styles, including the Arts and Crafts movement. His designs emphasized craftsmanship, simplicity, and the integration of buildings with their surroundings. In addition to his architectural work, Kinnersley has also been associated with several notable projects and buildings.

Then a specific metric is involved, sometimes we want to automatically add it to products.

E.g., in a context considering the common Minkowski inner product matrix where the $\eta$ 4x4 matrix and $\mu$ is a vector in ${\mathbb{R}}^4$which leads to the change of sign of some terms.

As of my last knowledge update in October 2021, Richard Peckover is not a widely recognized figure in popular culture, literature, or current events. It's possible that he could be a private individual or someone who has gained prominence after that date.

Charles Francis Mott (1875–1973) was an American businessman and philanthropist best known for his role as the co-founder of the General Motors Corporation and for his contributions to various charitable causes. Mott started his career in the automotive industry in the early 20th century and became an influential figure in the development of the auto manufacturing industry. In addition to his work with General Motors, Mott was known for his philanthropic efforts, particularly in the areas of education and health.

Ian Walmsley is a notable physicist known for his work in the fields of experimental quantum mechanics and optical physics. He has been involved in research related to quantum information processing and has made significant contributions to the understanding of light-matter interactions. As of my last knowledge update in October 2023, he held a position at the University of Oxford, where he has been involved in academic research and education.

James Robert Milne is a name that may refer to various individuals, but without additional context, it is not clear which specific person or entity you are referring to. If you could provide more details, such as relevant fields (e.g., science, arts, business) or significance, I would be able to offer more accurate information.

Joe Farman was a British scientist known for his significant contributions to climate science, particularly in the study of the ozone layer. He played a key role in the discovery of the Antarctic ozone hole in the 1980s. Farman, along with his colleagues at the British Antarctic Survey, conducted research that showed a dramatic seasonal decline in ozone levels over Antarctica, which was attributed to chlorofluorocarbons (CFCs) and other ozone-depleting substances.