This is beta site. https://beta.mathcity.org/ 2026-06-06T22:12:05+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/bsc/notes_of_mathematical_method/ch07_inner_product_spaces?rev=1737476035&do=diff Chapter 07: Inner Product Spaces Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Inner product spaces form and important topic of Functional Analysis. These are simply vector space over the field of real or complex numbers and with an inner product defined on them. text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/bsc/notes_of_mathematical_method/ch01_complex_numbers?rev=1737476035&do=diff Chapter 01: Complex Numbers [Chapter 01 Complex Numbers Methods] Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. A complex number is an element $(x,y)$ of the set $$ \mathbb{R}^2=\{(x,y): x,y \in \mathbb{R}\} $$ obeying the following rules of addition and multiplication.$z_1=(x_1,y_1)$$z_2=(x_2,y_2)$$z_1+z_2= (x_1+x_2, y_1+y_2)$$z_1 z_2 = (x_1 x_2 - y_1 y_2, x_1 y_2+y_1 x_2)$$\mathbb{R}^2$$\mathbb{C}$ text/html 2025-01-21T16:13:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/bsc/notes_of_mathematical_method/ch05_determinants?rev=1737476035&do=diff Chapter 05: Determinants * Determinant of a square matrix * Axiomatic definition of a determinant * Determinant as sum of products of elements * Determinant of the transpose * An algorithm to evaluate Det A * Determinants and inverse of matrices