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 ...
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Looking at these five examples where linear algebra comes up in physics, we see that for the first three, involving “classical physics”, we have vectors placed at different points in space and time. On the other hand, the fifth example is a vector space where the vectors are not to be thought of as being simple arrows in the normal, classical space of everyday life. In any case, it is clear tha...
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Nonnegative nilpotent lower triangular completions of a nonnegative nilpotent matrix are studied. It is shown that for every natural number between the index of the matrix and its order, there exists a completion that has this number as its index. A similar result is obtained for the rank. However, unlike the case of complex completions of complex matrices, it is proved that for every nonincrea...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2004
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2004.06.022