Linear Algebra and Its Applications, exercise 1.4.7

Exercise 1.4.7. Given the n-dimensional row vector y and column vector x, express their inner product in summation notation.

Answer: We have

yx = \begin{bmatrix} y_1&y_2&\cdots&y_n \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix} = y_1 x_1 + y_2 x_2 + \cdots + y_n x_n = \sum_{i = 1}^{i = n} y_i x_i

NOTE: This continues a series of posts containing worked out exercises from the (out of print) book Linear Algebra and Its Applications, Third Edition by Gilbert Strang.

If you find these posts useful I encourage you to also check out the more current Linear Algebra and Its Applications, Fourth Edition, Dr Strang’s introductory textbook Introduction to Linear Algebra, Fourth Edition and the accompanying free online course, and Dr Strang’s other books.

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