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What is the difference between the Frobenius norm and the 2-norm of a . . . For example, in matlab, norm (A,2) gives you induced 2-norm, which they simply call the 2-norm So in that sense, the answer to your question is that the (induced) matrix 2-norm is $\le$ than Frobenius norm, and the two are only equal when all of the matrix's eigenvalues have equal magnitude
What is the norm of a complex number? [duplicate] In number theory, the "norm" is the determinant of this matrix In that sense, unlike in analysis, the norm can be thought of as an area rather than a length, because the determinant can be interpreted as an area (or volume in higher dimensions ) However, the area volume interpretation only gets you so far
2-norm vs operator norm - Mathematics Stack Exchange The operator norm is a matrix operator norm associated with a vector norm It is defined as $||A||_ {\text {OP}} = \text {sup}_ {x \neq 0} \frac {|A x|_n} {|x|}$ and different for each vector norm In case of the Euclidian norm $|x|_2$ the operator norm is equivalent to the 2-matrix norm (the maximum singular value, as you already stated) So every vector norm has an associated operator norm
normed spaces - The difference between $L_1$ and $L_2$ norm . . . The $1$-norm and $2$-norm are both quite intuitive The $2$-norm is the usual notion of straight-line distance, or distance ‘as the crow flies’: it’s the length of a straight line segment joining the two points
Understanding L1 and L2 norms - Mathematics Stack Exchange I am not a mathematics student but somehow have to know about L1 and L2 norms I am looking for some appropriate sources to learn these things and know they work and what are their differences I am
Why is that the matrix $1$-norm and $\infty$-norm are equal to the . . . However, this post seems to shatter my assumption: 2-norm vs operator norm Upon further examination, it seems that the operator norm and matrix norm only coincide (=) for the matrix $1$ -norm or the matrix $\infty$ -norm (and extremely limited cases for matrix $2$ -norm) Why is this so?
How do I find the norm of a matrix? - Mathematics Stack Exchange I learned that the norm of a matrix is the square root of the maximum eigenvalue multiplied by the transpose of the matrix times the matrix Can anybody explain to me in further detail what steps I need to do after finding the maximum eigenvalue of the matrix below?
Meaning of the spectral norm of a matrix - Mathematics Stack Exchange The spectral norm (also know as Induced 2-norm) is the maximum singular value of a matrix Intuitively, you can think of it as the maximum 'scale', by which the matrix can 'stretch' a vector The maximum singular value is the square root of the maximum eigenvalue or the maximum eigenvalue if the matrix is symmetric hermitian