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SELFMADE
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I need help understanding this notation, what does this mean?
Squared of 2-norm?
1. Homework Statement
Thanks
Squared of 2-norm?
1. Homework Statement
Thanks
SELFMADE said:Thank you for your reply. So my hunch was right.
I am learning Machine Learning by myself. I have BSEE but I am encountering many symbols/notations that I don't understand.
For example, what does the "1 with a vertical line through its back" mean?
I know as far as E stands for expected value.
Thanks
A norm is a mathematical concept that measures the size or length of a vector in a vector space. It assigns a positive value to each vector, with the value of zero only assigned to the zero vector. Norms are commonly used in various fields of mathematics, such as linear algebra, functional analysis, and differential equations.
While both norms and metrics are mathematical concepts that measure distance or size, they differ in their definitions and properties. A norm is a function that maps a vector to a positive value, while a metric is a function that maps two points to a non-negative value. Additionally, norms are defined on vector spaces, while metrics are defined on general sets.
Some of the commonly used norms in mathematics include the Euclidean norm, also known as the 2-norm, the Manhattan norm, also known as the 1-norm, and the maximum norm, also known as the infinity norm. Other popular norms include the p-norm, where p is any positive real number, and the Frobenius norm, also known as the matrix norm.
The 2-norm of a vector, also known as the Euclidean norm, can be calculated by taking the square root of the sum of the squares of each element in the vector. In other words, if a vector is represented by (x1, x2, ..., xn), its 2-norm can be calculated as √(x1^2 + x2^2 + ... + xn^2).
Norms are important in mathematics because they provide a way to measure the size or length of vectors, which are fundamental objects in many mathematical fields. They also have various properties and applications, such as in optimization problems, functional analysis, and statistics. Norms also help to define important concepts such as convergence and continuity in mathematics.