Inner Product Space

library(Matrix)

library(ggplot2)

v1 <- c(1+2i, 3-4i, 5+6i)
v2 <- c(2+3i, 4-5i, 6+7i)

inner_product <- Conj(v1) %*% v2

print(inner_product)

##        [,1]
## [1,] 112-1i

vector_df <- data.frame(Re1 = Re(v1), Im1 = Im(v1),
                        Re2 = Re(v2), Im2 = Im(v2))

ggplot(vector_df) +
  geom_segment(aes(x = 0, y = 0, xend = Re1, yend = Im1, color = "v1"), arrow = arrow(length = unit(0.2, "cm"))) +
  geom_segment(aes(x = 0, y = 0, xend = Re2, yend = Im2, color = "v2"), arrow = arrow(length = unit(0.2, "cm"))) +
  geom_point(aes(x = Re1, y = Im1), color = "blue") +
  geom_point(aes(x = Re2, y = Im2), color = "red") +
  labs(x = "Real", y = "Imaginary") +
  theme_minimal() +
  scale_color_manual(values = c("v1" = "blue", "v2" = "red"))