Recent content by chadpip

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    Technicality of describing where sqrt(x) is increasing

    When describing where $sqrt{x}$ (square root of x) is increasing, it's from zero to infinity. But, do you say (0,inf) or [0, inf) ? (I'm tutoring a student in pre-calc, and this came up. They don't know any calculus.) In a situation like where is $x^2$ inc/dec, we'd say inc: (0, inf)...
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    What is an example of a well conditioned matrix with a small determinant?

    oh sorry! i must have overlooked that in the rules :( but..the good news is i finally figured one out! so forget this question
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    What is an example of a well conditioned matrix with a small determinant?

    this is more of a numerical analysis question..so I am not sure where to post it..(also put it up in the computers forum) im wondering, I've seen examples of ill conditioned matrices with small determinants...but what would be an example of a well conditioned matrix with a very small...
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    Lin algebra: find the matrix with respect to basis

    would then matrix then just be: 0 -1 1 0 ?
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    Lin algebra: find the matrix with respect to basis

    ah okay. then: T(f_1) = - f_2 and T(f_2) = f_1 .i feel we are now ready to construct the matrix knowing this but i am not sure what it is yet. I am thinking
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    Lin algebra: find the matrix with respect to basis

    since T is linear, T(V) = T(e1 - e4) = T(e1) - T(e4) = -e1 -e2 + e3 T(e1 + e2 - e3) = T(e1) -T(e2) + T(e3) = e1 - e4 the results come out of elements of the span, or linear combinations of elements of the span of V. therefore, T(V) is contained in V, so T maps V into itself..
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    Lin algebra: find the matrix with respect to basis

    Homework Statement Let W be a 4dim vector space with basis {e1, e2, e3, e4}. Let T be the linear mapping: T(e1) = -e1 -2e2 + 2e3 T(e2) = 4e1 + 4e2 - 5e3 -3e4 T(e3) = 2e1 + 2e2 -3e3 -2e4 T(e4) = -e2 + e3 Let V be the subspace spanned by {e1 + e2 - e3, e1 - e4, -e1 + e2 -e3 +2e4} Now: find a...
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