snesnerd said:Let x = (2,1+i,i) and y = (2-i,2,1+2i). Find <x,y>
So my work is the following:
2(2-i) + (1+i)2 + i(1+2i) = 4+i, but my book says the correct answer is 8+5i. Hmmm what am I doing wrong?
An inner product space is a mathematical structure that consists of a vector space equipped with an inner product, which is a mathematical operation that takes two vectors as inputs and produces a scalar as output. This operation satisfies certain properties, such as linearity and symmetry, and allows for the measurement of the angle between two vectors.
An inner product space is a type of vector space, but with the added structure of an inner product. This means that in addition to the usual operations of addition and scalar multiplication, an inner product space also has the ability to measure angles and distances between vectors.
To find
The complex number in "8+5i" represents the coefficients of the two vectors, x and y, in the inner product operation. In an inner product space, the inner product is typically defined as the sum of the products of the corresponding components of the two vectors. In this case, 8 and 5 represent the coefficients of the real and imaginary components of the vectors, respectively.