LINEAR ALGEBRA

Vasileios Zikos

Chapter 1 in Essential Mathematics for Economics:A Student's Guide to Key Mathematical Techniques, 2026, pp 1-23 from World Scientific Publishing Co. Pte. Ltd.

Abstract: After completing this chapter, students will be able to:Understand necessary and sufficient conditions.Perform matrix operations.Derive the transpose of a matrix.Derive the inverse of a matrix.Calculate cofactors and determinants.This chapter focuses on the study of necessary and sufficient conditions, as well as the basic concepts of matrix algebra. It begins by explaining the distinction between necessary and sufficient conditions, and how they describe the relationship between two statements. The chapter then introduces the basic elements of matrix algebra, emphasizing concepts that will be useful later in the book, especially for solving optimization problems.

Keywords: Microeconomics; Applied Microeconomics; Optimization; First-order Conditions; Second-order Conditions; Equality Constraints; Inequality Constraints; Concavity; Convexity; Matrix Algebra; Determinants; Differential Calculus; Integral Calculus; First-order Linear Differential Equations; Utility Maximization; Profit Maximization; Research Applications (search for similar items in EconPapers)
JEL-codes: C01 C02 C61 D00 (search for similar items in EconPapers)
Date: 2026
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