Universal Identities I
... complicated identities, such as in linear algebra, where the polynomial identity viewpoint is really useful thanks to the following theorem involving complex numbers. Notice the (non-algebraic) topological hypothesis which occurs. Theorem 2.6. Let f (X1 , . . . , Xn ) and g(X1 , . . . , Xn ) be in C ...
... complicated identities, such as in linear algebra, where the polynomial identity viewpoint is really useful thanks to the following theorem involving complex numbers. Notice the (non-algebraic) topological hypothesis which occurs. Theorem 2.6. Let f (X1 , . . . , Xn ) and g(X1 , . . . , Xn ) be in C ...
Linear Combinations and Linear Independence – Chapter 2 of
... Similarly, Euclidean 3-space, denoted R3 , is the set of all vectors with three real-valued entries: ...
... Similarly, Euclidean 3-space, denoted R3 , is the set of all vectors with three real-valued entries: ...
Extremal properties of ray-nonsingular matrices
... we say that A ◦ X has ray-pattern A. In this paper we address the following question, which is posed in [7]: For which n, does there exist a full n × n ray-nonsingular matrix? The corresponding problem for sign-nonsingular matrices was originally posed by Polya [8], and there are numerous ways to s ...
... we say that A ◦ X has ray-pattern A. In this paper we address the following question, which is posed in [7]: For which n, does there exist a full n × n ray-nonsingular matrix? The corresponding problem for sign-nonsingular matrices was originally posed by Polya [8], and there are numerous ways to s ...
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