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Rroam reacted to PeroK's post in the thread Conflicting definitions of linear independence with
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You are given three vectors, which are linearly independent. If you add a 4th vector, the zero vector, then that extended set of... -
RIf you turn your vectors into an nxm matrix; ##n \neq m##, then the vectors are dependent iff(def.) the matrix doesn't have maximal...
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Rroam reacted to FactChecker's post in the thread Conflicting definitions of linear independence with Like.
The second statement is not a "definition" of independence, it is a statement of (a proposed) fact about independence.
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Rroam reacted to Mark44's post in the thread Conflicting definitions of linear independence with Like.
That was in reference to your example. If you have 5 vectors in ##\mathbb R^4##, they can't possibly be a linearly independent set. But...
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RWhy are ##A,B## closed in ##H##? If so, then they are closed in ##S,## too: The boundary of ##A## in ##S## is contained in ##H## and...
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RI took a quick look at that book and wondered why you were interested in such a tedious approach to topology. Then I noticed some very...
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Rroam reacted to HallsofIvy's post in the thread Can You Determine the Gradient of an Unknown Function? with Like.
Adding two numbers and dividing by 2: (½(tan-1((f(x+1)–f(x))/10^10)+tan-1((f(x)–f(x-1))/10^10)) is averaging. What you are doing is...
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Rroam reacted to HallsofIvy's post in the thread Can You Determine the Gradient of an Unknown Function? with Like.
First, a lot of people won't open a ".doc" file from someone they don't know for fear of computer viruses- attaching such files is not a...