Bilinear formIn mathematics, a bilinear form is a bilinear map V × V → K on a vector space V (the elements of which are called vectors) over a field K (the elements of which are called scalars). In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) The dot product on is an example of a bilinear form.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
Nicholas SparksNicholas Charles Sparks (born December 31, 1965) is an American romance novelist, screenwriter, and film producer. He has published twenty-three novels, all New York Times bestsellers, and two works of non-fiction, with over 115 million copies sold worldwide in more than 50 languages. Among his works are The Notebook, A Walk to Remember, and Message in a Bottle which, along with eight other books, have been adapted as feature films. Sparks lives in North Carolina, where many of his novels are set.
Jan MayenJan Mayen (jɑn ˈmɑ̀ɪən) is a Norwegian volcanic island in the Arctic Ocean with no permanent population. It is long (southwest-northeast) and in area, partly covered by glaciers (an area of around the Beerenberg volcano). It has two parts: larger northeast Nord-Jan and smaller Sør-Jan, linked by a wide isthmus. It lies northeast of Iceland (495 km [305 mi] NE of Kolbeinsey), east of central Greenland, and northwest of Vesterålen, Norway. The island is mountainous, the highest summit being the Beerenberg volcano in the north.
Symmetric matrixIn linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, Because equal matrices have equal dimensions, only square matrices can be symmetric. The entries of a symmetric matrix are symmetric with respect to the main diagonal. So if denotes the entry in the th row and th column then for all indices and Every square diagonal matrix is symmetric, since all off-diagonal elements are zero. Similarly in characteristic different from 2, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.
