linear algebra - What is the norm of a complex number?
2013年1月24日 · We can define the norm of a complex number in other ways, provided they satisfy the following properties. Positive homogeneity. Triangle inequality. Zero norm iff zero vector. We could define a $3$-norm where you sum up all the components cubed and take the cubic root. The infinite norm simply takes the maximum component's absolute value as the ...
How are norms different from absolute values? - Mathematics …
$\begingroup$ Norm (mathematics) facts for kids. It's not for kids actually, and certainly more concise and helpful than Wikipedia. ("For the real numbers, the only norm is the absolute value. For spaces with more dimensions, the norm can be …
matrices - Orthogonal matrix norm - Mathematics Stack Exchange
2016年4月22日 · The original question was asking about a matrix H and a matrix A, so presumably we are talking about the operator norm.
Understanding L1 and L2 norms - Mathematics Stack Exchange
2021年2月6日 · You ask about the L1 and L2 norms. The L1 norm is the sum of the absolute value of the entries in the vector. The L2 norm is the square root of the sum of the squares of entries of the vector. In general, the Lp norm is the pth root of the sum of the entries of the vector raised to the pth power.
inequality - Zero "norm" properties - Mathematics Stack Exchange
is a semi-norm because it does not satisfy all properties of a norm. This is a misuse of the term seminorm, which is defined as a norm, except that it's okay for a nonzero element to have seminorm $0$. The cardinality of support satisfies the triangle inequality, since the support of the sum of two vectors is contained in the union of their ...
linear algebra - The difference between norm and modulus
2014年4月16日 · Modulus is the term specifically used for complex numbers (scalars), and reduces to the concept of absolute value when referring to real numbers. When viewing a complex number as a real pair in the complex plane, then modulus corresponds to the (euclidian) norm on $\mathbb{R}^2$.
2-norm vs operator norm - Mathematics Stack Exchange
So every vector norm has an associated operator norm, for which sometimes simplified expressions as exist. The Frobenius norm (i.e. the sum of singular values) is a matrix norm (it fulfills the norm axioms), but not an operator norm, since no vector norm exists so that the above definition for the operator norm matches the Frobenius norm.
Who introduced the term "norm" into mathematics?
2013年8月12日 · According to Steven Schwartzman's The Words of Mathematics, "norm" derives from the Latin norma meaning "carpenter's square", which explains its meaning of perpendicularity and measuring a unit. According to Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics , "norm" was first used in number theory by Gauss in 1832, for the ...
Simple explanation of uniform norm / sup-norm? - Mathematics …
2017年12月17日 · I've read the Uniform Norm Wikipedia page, but my most of it went over my head. What is the sup-norm in simple and / or intuitive terms? Are there any good examples which illustrate it?
Intuitive explanation of $L^2$-norm - Mathematics Stack Exchange
Differences between the L1-norm and the L2-norm . In mathematics, ...