Stanford ENGR108: Introduction to Applied Linear Algebra  2020  Lecture 18VMLS matrix vector mult  Summary and Q&A
TL;DR
Matrixvector multiplication is a fundamental operation used throughout the book and class, with applications in various contexts.
Questions & Answers
Q: What is matrixvector multiplication?
Matrixvector multiplication involves multiplying an m by n matrix with an ndimensional vector to produce an mdimensional vector. It can be interpreted as taking the inner product of each row of the matrix with the vector.
Q: How is matrixvector multiplication denoted?
Matrixvector multiplication is denoted by concatenating the matrix symbol and the vector symbol, such as Ax. This represents the product of the matrix and vector.
Q: How can matrixvector multiplication be interpreted in terms of rows and columns?
Matrixvector multiplication can be interpreted as taking the inner product of each row of the matrix with the vector or as a linear combination of the columns of the matrix using the coefficients from the vector.
Q: What are some applications of matrixvector multiplication?
Matrixvector multiplication can be used to compute row sums of a matrix, column sums of a matrix, and pick out specific columns of a matrix. It is also fundamental in representing linear combinations and determining linear independence of the columns of a matrix.
Summary & Key Takeaways

Matrixvector multiplication is performed by multiplying an m by n matrix with an ndimensional vector.

The result of matrixvector multiplication is an mdimensional vector that can be computed by taking the inner product of each row of the matrix with the vector.

Matrixvector multiplication can be interpreted as taking the inner product of each row of the matrix with the vector or as a linear combination of the columns of the matrix using the coefficients from the vector.