### Linear algebra c-3

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DGBMV - banded matrix vector multiply. DSYMV - symmetric matrix vector multiply. DSBMV - symmetric banded matrix vector multiply.

DSPMV - symmetric packed matrix vector multiply. DTRMV - triangular matrix vector multiply. DTBMV - triangular banded matrix vector multiply. DTPMV - triangular packed matrix vector multiply. DTRSV - solving triangular matrix problems. DTBSV - solving triangular banded matrix problems. DTPSV - solving triangular packed matrix problems. CGEMV - matrix vector multiply. CGBMV - banded matrix vector multiply. CHEMV - hermitian matrix vector multiply. CHBMV - hermitian banded matrix vector multiply.

CHPMV - hermitian packed matrix vector multiply. CTRMV - triangular matrix vector multiply. CTBMV - triangular banded matrix vector multiply. CTPMV - triangular packed matrix vector multiply. CTRSV - solving triangular matrix problems. CTBSV - solving triangular banded matrix problems.

CTPSV - solving triangular packed matrix problems. CHER2 - hermitian rank 2 operation. CHPR2 - hermitian packed rank 2 operation. ZGEMV - matrix vector multiply. ZGBMV - banded matrix vector multiply. ZHEMV - hermitian matrix vector multiply. ZHBMV - hermitian banded matrix vector multiply.

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ZHPMV - hermitian packed matrix vector multiply. ZTRMV - triangular matrix vector multiply. ZTBMV - triangular banded matrix vector multiply. ZTPMV - triangular packed matrix vector multiply.

## BLAS (Basic Linear Algebra Subprograms)

ZTRSV - solving triangular matrix problems. ZTBSV - solving triangular banded matrix problems. ZTPSV - solving triangular packed matrix problems.

ZHER2 - hermitian rank 2 operation. ZHPR2 - hermitian packed rank 2 operation. SGEMM - matrix matrix multiply. SSYMM - symmetric matrix matrix multiply. SSYRK - symmetric rank-k update to a matrix. SSYR2K - symmetric rank-2k update to a matrix. STRMM - triangular matrix matrix multiply. STRSM - solving triangular matrix with multiple right hand sides. DGEMM - matrix matrix multiply. DSYMM - symmetric matrix matrix multiply. DSYRK - symmetric rank-k update to a matrix. DSYR2K - symmetric rank-2k update to a matrix.

DTRMM - triangular matrix matrix multiply. DTRSM - solving triangular matrix with multiple right hand sides.

CGEMM - matrix matrix multiply. CSYMM - symmetric matrix matrix multiply. CHEMM - hermitian matrix matrix multiply. CSYRK - symmetric rank-k update to a matrix. CHERK - hermitian rank-k update to a matrix.

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CSYR2K - symmetric rank-2k update to a matrix. CHER2K - hermitian rank-2k update to a matrix. CTRMM - triangular matrix matrix multiply. CTRSM - solving triangular matrix with multiple right hand sides. ZGEMM - matrix matrix multiply. ZSYMM - symmetric matrix matrix multiply. ZHEMM - hermitian matrix matrix multiply. We can get around this problem by shifting around the orientation of the vectors making up the lines of each small patch by changing our co-ordinate system, in the same way that we define a parametric surface.

However, if we do that then, it becomes harder to conceptualize what the surface area of the shape will be. The area does not remain constant, it actually changes as the shape contracts and expands as the orientation of the lines change around. Another way to think about area, then, is with the normal vector.

### Operations with Matrices

On face value these two things do not seem to be related. After all the normal vector is just a vector that sticks out from the shape, perpendicular to its surface. But remember that the normal vector has a magnitude like any other vector and its magnitude is actually proportionate to the lengths of the vectors that made up its cross product.

As it turns out, the normal vector becomes a proxy for working out the area of a quadrialteral defined by two vectors. If the normal vector is short, then the area will be quite small. If the normal vector is long, then the area will be larger. Astute readers may recognize the link between the normal vector defined as the cross product between two vectors and the determinant of a square 3x3 matrix. Back to surface areas, we reformulate the problem in another way - divide up the surface into small patches and then add up the magnitude of their normal vectors.

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