From linear algebra via affine algebra to projective algebra
نویسندگان
چکیده
منابع مشابه
The Algebra of Linear Algebra
3. You are already familiar with the concept of vector spaces in the form of nite dimensional Euclidean vector spaces, and most of what we do in these lectures will involve these spaces (and, indeed, will also assume that the dot product operation is well-de ned so that we can de ne the matrix operations associated with linear transformations). However, it will also be useful to consider some ...
متن کاملThe Fundamental Theorem of Algebra via Linear Algebra
Theorem 2 is also consequence of Theorem 1, so the two theorems are equivalent. In fact, the implication Theorem 1 ⇒ Theorem 2 is usually how one first meets the fundamental theorem of algebra in a linear algebra course: it assures us that any complex square matrix has an eigenvector because the characteristic polynomial of the matrix has a complex root. But here, we will prove Theorem 2 withou...
متن کاملFrom Satisfiability to Linear Algebra
Satisfiability of boolean formulas (SAT) is an interesting problem for many reasons. It was the first problem proved to be NP-complete by Cook. Efficient SAT solvers have many applications. In fact, there is a huge literature on SAT, and its connections with other optimization problems have been explored. In this paper, we look at SAT using linear algebra, a basic and fundamental mathematics th...
متن کاملbiquaternions lie algebra and complex-projective spaces
in this paper, lie group structure and lie algebra structure of unit complex 3-sphere are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of and the special complex unitary matrices (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers . the relat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2003.06.021