Recent questions tagged trace

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Why should levels of carbon and greenhouse gases in the atmosphere be reduced?
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How can businesses leverage customer trace data?
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What is customer trace data and why is it valuable?
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What is the rank of a matrix?
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One writes 268 numbers around a circle such that the sum of 20 consecutive numbers is always equal to 75 . The numbers 3,4 and 9 are written in positions 17,83 and 144 re...
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30 numbers \(a_{1}, \ldots, a_{30}\) are written along the circle in such a way that each of them is equal to the absolute value of the difference between the next two in...
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If carbon dioxide is a trace gas in our atmosphere, why does it matter?
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Let \(A=\left(a_{i j}\right)\) be an \(n \times n\) matrix with the property that its absolute row sums are at most 1 , that is, \(\left|a_{i 1}\right|+\cdots+\left|a_{\t...
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Let \(A\) be a square matrix and let \(\|B\|\) be any norm on matrices [one example is \(\left.\|B\|=\max _{i, j}\left|b_{i j}\right|\right]\). To what extent are the con...
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Let \(\alpha_{1}, \ldots, \alpha_{n}\) be positive real numbers and let \(A=\left(a_{i j}\right)\) where \(a_{i j}=\alpha_{i} / \alpha_{j} .\) Say as much as you can abou...
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Every real upper triangular \(n \times n\) matrix \(\left(a_{i j}\right)\) with \(a_{i i}=1, i=1,2, \ldots, n\) is invertible. Proof or counterexample.
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Let \(A\) be the rank one \(n \times n\) matrix \(A=\left(v_{i} v_{j}\right)\), where \(\vec{v}:=\left(v_{1}, \ldots, v_{n}\right)\) is a non-zero real vector.a) Find its...
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Let \(A=\left(a_{i j}\right)\) be an \(n \times n\) matrix whose rank is 1 . Let \(v:=\left(v_{1}, \ldots, v_{n}\right) \neq 0\) be a basis for the image of \(A\).a) Show...
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The trace of a square matrix is ...
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Every command fails with command not found. How do you trace the source of the error and resolve it?
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