By Géza Schay
Building at the author's past variation at the topic (Introduction toLinear Algebra, Jones & Bartlett, 1996), this e-book bargains a refreshingly concise textual content compatible for the standard direction in linear algebra, offering a delicately chosen array of crucial subject matters that may be completely lined in one semester. even supposing the exposition often falls according to the cloth steered through the Linear Algebra Curriculum research crew, it significantly deviates in supplying an early emphasis at the geometric foundations of linear algebra. this provides scholars a extra intuitive realizing of the topic and permits a neater grab of extra summary recommendations lined later within the direction.
The concentration all through is rooted within the mathematical basics, however the textual content additionally investigates a couple of attention-grabbing functions, together with a bit on special effects, a bankruptcy on numerical tools, and plenty of routines and examples utilizing MATLAB. in the meantime, many visuals and difficulties (a entire ideas handbook is accessible to teachers) are incorporated to augment and strengthen knowing through the publication.
Brief but specific and rigorous, this paintings is a perfect selection for a one-semester path in linear algebra precise essentially at math or physics majors. it's a useful device for any professor who teaches the subject.
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Additional resources for A Concise Introduction to Linear Algebra
Using dot products, prove the Theorem of Thales: If we take a point P on a circle and form a triangle by joining it to the opposite ends of an arbitrary diameter, then the angle at P is a right angle. ) P p -r r O Fig. 20. 12. 1, (p − λq) · (p − λq) ≥ 0 for every scalar λ. Expand the left-hand side to obtain a quadratic function of λ. The graph of this function is a parabola above the λ-axis. Find the λ-value of the lowest point in terms of p and q, substitute it into the inequality, and simplify.
The area of the triangle. 9. Decompose the vector p = (2, −3, 1) into components parallel and perpendicular to the vector q = (12, 3, 4). 10. 54) for all vectors in Rn . Interpret geometrically! 11. Using dot products, prove the Theorem of Thales: If we take a point P on a circle and form a triangle by joining it to the opposite ends of an arbitrary diameter, then the angle at P is a right angle. ) P p -r r O Fig. 20. 12. 1, (p − λq) · (p − λq) ≥ 0 for every scalar λ. Expand the left-hand side to obtain a quadratic function of λ.
31. Between the point P0 (1, −2, 4) and the line p = (3, 2, −4) + s(7, −5, 4). 32. 83 in R2 ? Make a drawing and explain. 33. Let the equation of a plane S be given in R3 in the form n · p = d, with |n| = 1. Let us deﬁne a function by f (q) = n · q − d, where q is the position vector of any point Q in R3 , whether in S or not. Show that the value of f (q) equals the signed distance of Q from S, which is positive if n points from S towards Q, and negative if n points from Q towards S. 34. 33. 35.
A Concise Introduction to Linear Algebra by Géza Schay