Within the The Holy Trinity of popular Brazilian music, Caetano has the most New Age religious feel to him. He is also perhaps the most varied of the trinity however, also covering heavier topics at times.
Elements of the orthogonal group have determinant plus or minus one Updated 2025-01-10 +Created 1970-01-01
What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms Updated 2025-01-10 +Created 1970-01-01
We looking at the definition the orthogonal group is the group of all matrices that preserve the dot product, we notice that the dot product is one example of positive definite symmetric bilinear form, which in turn can also be represented by a matrix as shown at: Section "Matrix representation of a symmetric bilinear form".
By looking at this more general point of view, we could ask ourselves what happens to the group if instead of the dot product we took a more general bilinear form, e.g.:The answers to those questions are given by the Sylvester's law of inertia at Section "All indefinite orthogonal groups of matrices of equal metric signature are isomorphic".
- : another positive definite symmetric bilinear form such as ?
- what if we drop the positive definite requirement, e.g. ?
Uploaded at: uploads.worldlibrary.net/uploads/pdf/20130423230739the_outlaws_of_the_marsh_pdf.pdf TODO legality? World Library seems like a legit website. Reads "Copyrighted materials".
"The Capital" is what now is Kaifeng in Shandong, and it used to be the capital during the (Northern) Song dynasty.
In the novel it is simply often simply called as 东京 (capital of the East), which is now highly ambiguous term that can indicate several different historical capitals! Notably it is the name of modern tokyo.
The term "Mount Liang" generally refers to both the mountain and the surrounding marshy areas.
The novel always uses the term "梁山泊' (liang2 shan1 po1) to refer to the place.
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