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Tutor profile: Matthew F.

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Matthew F.
PhD in Operations Research and Applied Math background
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Questions

Subject: Linear Programming

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Question:

Assign $$m$$ workers to $$n$$ tasks while minimizing the cost of the assignment.

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Matthew F.
Answer:

To formulate this linear program we have: $$min \sum_i \sum_j c_{ij}x_{ij}$$ such that all workers are assigned to a job and vice versa $$\sum_{i=1}^m x_{ij}=1, \quad \forall j$$ $$\sum_{j=1}^n x_{ij}=1, \quad \forall i$$

Subject: Applied Mathematics

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Question:

What do eigenvalues tell you about a matrix?

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Matthew F.
Answer:

In statistics, eigenvalues tell you how much variation there is in the data when doing PCA. In nonlinear optimization, positive eigenvalues indicate that a matrix is positive definite, which tells you whether or not you have a global max or min.

Subject: Calculus

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Question:

What is a derivative?

Inactive
Matthew F.
Answer:

Derivatives tell you how fast a function is changing at a particular input value. It's also known as a rate of change. For example, $$f'(x)=\frac{d}{dx}(x^2)=2x$$. For $$x=1$$, the aforementioned function is changing at a rate of 2 units (i.e. $$f'(1)=2(1)=2$$).

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