# Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 18-VMLS matrix vector mult | Summary and Q&A

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February 26, 2021
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Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 18-VMLS matrix vector mult

## TL;DR

Matrix-vector multiplication is a fundamental operation used throughout the book and class, with applications in various contexts.

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### Q: What is matrix-vector multiplication?

Matrix-vector multiplication involves multiplying an m by n matrix with an n-dimensional vector to produce an m-dimensional vector. It can be interpreted as taking the inner product of each row of the matrix with the vector.

### Q: How is matrix-vector multiplication denoted?

Matrix-vector 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 matrix-vector multiplication be interpreted in terms of rows and columns?

Matrix-vector 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 matrix-vector multiplication?

Matrix-vector 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

• Matrix-vector multiplication is performed by multiplying an m by n matrix with an n-dimensional vector.

• The result of matrix-vector multiplication is an m-dimensional vector that can be computed by taking the inner product of each row of the matrix with the vector.

• Matrix-vector 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.