# Tag Archives: function space

## Linear Algebra and Its Applications, Exercise 3.4.25

Exercise 3.4.25. Given over the interval what is the closest line to the parabola formed by ? Answer: This amounts to finding a least-squares solution to the equation , where the entries 1, , and are understood as functions of … Continue reading

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## Linear Algebra and Its Applications, Exercise 3.4.23

Exercise 3.4.23. Given the step function with for and for , find the following Fourier coefficients: Answer: For the numerator is and the denominator is so that . For the numerator is so that . For the numerator is and … Continue reading

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## Linear Algebra and Its Applications, Exercise 3.4.21

Exercise 3.4.21. Given the function on the interval , what is the closest function to ? What is the closest line to ? Answer: To find the closest function to the function we first project onto the function on the … Continue reading

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