# LinearAlgebraOperationsExtensions.SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>) Method

Performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

## Definition

Namespace: Extreme.Collections
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 9.0.0
C#
``````public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
Span2D<T> a
)
``````

#### Parameters

operations  ILinearAlgebraOperations<T>

uplo  MatrixTriangle
```             On entry, UPLO specifies whether the upper or lower
triangular part of the array A is to be referenced as
follows:
UPLO = 'U' or 'u'   Only the upper triangular part of A
is to be referenced.
UPLO = 'L' or 'l'   Only the lower triangular part of A
is to be referenced.
```
n  Int32
```             On entry, N specifies the order of the matrix A.
N must be at least zero.
```
alpha  T
```            ALPHA is DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha.
```
```            X is DOUBLE PRECISION array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
```
```             On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
```
a  Span2D<T>
```            A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
Before entry with  UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of A is not referenced. On exit, the
upper triangular part of the array A is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of A is not referenced. On exit, the
lower triangular part of the array A is overwritten by the
lower triangular part of the updated matrix.
```
```             On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
```

T

#### Usage Note

In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).

## Remarks

``` Further Details:            Level 2 LinearAlgebra routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Authors:
Univ. of Tennessee,
Univ. of California Berkeley,