norm, singular value

"Norm"
Format: N=norm (a,p)
Function: Norm function can calculate several different types of matrix norm, according to different p can get different norm
The following is the explanation of help norm in MATLAB
NORM Matrix or vector NORM.
for matrices ...
NORM (x) is the largest singular value of X, Max (SVD (x)).
NORM (x,2) is the same as NORM (X).
NORM (x,1) is the 1-norm of X, the largest column sum,
= max (SUM (ABS (X))).
NORM (X,inf) is the Infinity NORM of X, the largest row sum,
= max (SUM (ABS (X))).
NORM (x, ' fro ') is the Frobenius NORM, sqrt (SUM (diag (x ' *x)).
NORM (x,p) is available for the matrix X only if P is 1, 2, INF or ' fro '.
for vectors ...
NORM (v,p) = SUM (ABS (V). ^p) ^ (1/p).
NORM (V) = NORM (v,2).
NORM (V,inf) = MAX (ABS (V)).
NORM (v,-inf) = MIN (abs (V)).
1, if A is a matrix
N=norm (a), returns the maximum singular value of a, that is, Max (SVD (A))
N=norm (a,p), depending on p, return different values
P return value
1 returns the largest column in a and, that is, Max ( ABS (a)))
2 Returns the maximum singular value of a, the same as N=norm (a) Usage
INF returns the largest row in a and, that is, Max (SUM (ABS (A)))
Fro ' returns the diagonal and square root of the product of a and a ', that is, sqrt (sum ( Diag (A ' *a)))

2. If a is a vector
Norm (a,p) returns the P-norm of vector A. That is, return sum (ABS (A). ^p) ^ (1/p), to any p greater than 1 less than positive infinity;
Norm (a) returns the 2 norm of Vector A, which is equivalent to Norm (a,2), which is sum (ABS (a). ^2) ^ (1/2)
Norm (A,inf) returns MAX (ABS (A))
Norm (A,-inf) return min (ABS (A))
"Singular value"
Format: [U,s,v] = SVD (X)
Explanation: [U,s,v] = SVD (X) produces a diagonal matrix S of the same dimension as X, with nonnegative diagonal elements in Decrea Sing order, and unitary matrices U and V so that X = U*s*v '.
Assuming that X is the MN matrix, then S is the singular value matrix, which is the m*n-order diagonal matrix, whose diagonal value is the arithmetic square root of the nonnegative eigenvalues of x^* X; U is the m*m-order unitary matrix, which is the eigenvector of x*x^ (conjugate transpose of x); V is the n*n-order unitary matrix, which is x^ characteristic vectors of x;

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norm, singular value