Matrices

What you will learn

• Multiply a matrix by a vector
• Read a transpose
• Determine product dimensions

Reasoning habits that help

• Each component of a matrix-vector product is a row-column dot product.
• Transposition reflects entries across the main diagonal by interchanging their indices.
• Matrix multiplication is conformable when the inner dimensions match, and the result takes the outer dimensions.

Where economists use these methods

• Matrix-vector products aggregate input-output requirements, portfolio returns, and systems of linear predictions.
• Transposes reorganize economic data and appear in regression formulas, quadratic forms, and matrix derivatives.
• Dimension checks prevent invalid matrix operations in econometrics, input-output analysis, and multivariate models.

Helpful prerequisites

Systems of Linear Equations