LAFF What you will learn

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Subsection 4.1.3 What you will learn

Upon completion of this unit, you should be able to

Make use of partitioning to perform matrix vector multiplication.
Transpose a partitioned matrix.
Take advantage of special structures to perform matrix-vector multiplication with triangular and symmetric matrices.
Express and implement various matrix-vector multiplication algorithms using the FLAME notation and FlamePy.
Make connections between the composition of linear transformations and matrix-matrix multiplication.
Compute a matrix-matrix multiplication.
Recognize scalars and column/row vectors as special cases of matrices.
Compute common vector-vector and matrix-vector operations as special cases of matrix-matrix multiplication.
Compute an outer product \(x y^T \) as a special case of matrix-matrix multiplication and recognize that
- The rows of the resulting matrix are scalar multiples of \(y^T \text{.}\)
- The columns of the resulting matrix are scalar multiples of \(x \text{.}\)