Ĭhapter Five: Similarity Complex Vector Spaces. Topic: Speed of Calculating Determinants. Four.II.1: Determinants as Size Functions Laplace’s Formula. Īnswers to Exercises Geometry of Determinants. Four.I.3: The Permutation Expansion Four.I.4: Determinants Exist. Three.VI.2: Gram-Schmidt Orthogonalization. Three.VI.1: Orthogonal Projection Into a Line. Three.V.1: Changing Representations of Vectors.
Three.IV.3: Mechanics of Matrix Multiplication. Three.III.1: Representing Linear Maps with Matrices Three.III.2: Any Matrix Represents a Linear Map.
Three.I.2: Dimension Characterizes Isomorphism. Dimensional AnalysisĬhapter Three: Maps Between Spaces Isomorphisms. Linear Algebra, by Hefferon Topic: Topic: Topic: Topic:įields. Two.III.3: Vector Spaces and Linear Systems Two.III.4: Combining Subspaces. Ĭhapter Two: Vector Spaces Definition of Vector Space. One.I.3: General = Particular + Homogeneous Linear Geometry. Jim Hefferon Saint Michael’s College, Colchester VT USA 2014-Dec-25Ĭontents Chapter One: Linear Systems Solving Linear Systems. Contact information is on the book’s home page. That way, clicking on the question number in the book takes you to its answer and clicking on the answer number takes you to the question, I welcome bug reports and comments. If you have an electronic version of this file then save it in the same directory as the book. An answer labeled here as One.II.3.4 is for the question numbered 4 from the first chapter, second section, and third subsection. Preface These are answers to the exercises in Linear Algebra by J Hefferon. Name nu NEW xi KSIGH omicron OM-uh-CRON pi PIE rho ROW sigma SIG-muh tau TOW (as in cow) upsilon OOP-suh-LON phi FEE, or FI (as in hi) chi KI (as in hi) psi SIGH, or PSIGH omega oh-MAY-guhĬapitals shown are the ones that differ from Roman capitals. Name alpha AL-fuh beta BAY-tuh gamma GAM-muh delta DEL-tuh epsilon EP-suh-lon zeta ZAY-tuh eta AY-tuh theta THAY-tuh iota eye-OH-tuh kappa KAP-uh lambda LAM-duh mu MEWĬharacter ν ξ, Ξ o π, Π ρ σ, Σ τ υ, Υ φ, Φ χ ψ, Ψ ω, Ω Real numbers, positive reals, n-tuples of reals natural numbers, complex numbers open interval, closed interval sequence (a list in which order matters) row i and column j entry of matrix H vector spaces vector, zero vector, zero vector of a space V space of degree n polynomials, n×m matrices span of a set basis, basis vectors standard basis for Rn isomorphic spaces direct sum of subspaces homomorphisms (linear maps) transformations (linear maps from a space to itself) representation of a vector, a map zero matrix, identity matrix determinant of the matrix range space, null space of the map generalized range space and null space Greek letters with pronounciationĬharacter α β γ, Γ δ, ∆ ζ η θ, Θ ι κ λ, Λ µ , ~en i ∼W V= M⊕N h, g t, s RepB (~v), RepB,D (h) Zn×m or Z, In×n or I |T | R(h), N (h) R∞ (h), N∞ (h)
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