By Géza Schay

Building at the author's earlier version at the topic (*Introduction to**Linear Algebra*, Jones & Bartlett, 1996), this publication bargains a refreshingly concise textual content appropriate for the standard path in linear algebra, providing a gently chosen array of crucial subject matters that may be completely lined in one semester. even if the exposition more often than not falls in accordance with the fabric prompt via the Linear Algebra Curriculum learn team, it significantly deviates in offering an early emphasis at the geometric foundations of linear algebra. this offers scholars a extra intuitive realizing of the topic and allows a better take hold of of extra summary ideas lined later within the direction.

The concentration all through is rooted within the mathematical basics, however the textual content additionally investigates a couple of fascinating functions, together with a bit on special effects, a bankruptcy on numerical tools, and lots of routines and examples utilizing MATLAB. in the meantime, many visuals and difficulties (a entire ideas handbook is offered to teachers) are integrated to augment and make stronger realizing during the publication.

Brief but specific and rigorous, this paintings is a perfect selection for a one-semester direction in linear algebra particular essentially at math or physics majors. it's a precious software for any professor who teaches the subject.

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**Extra resources for A Concise Introduction to Linear Algebra**

**Example text**

A right triangle in terms of vectors Proof. Assume ﬁrst p ⊥ q. 15). 26) from which p · q = 0 follows at once. 24. 24 implies that the OP Q triangle is a right triangle with p ⊥ q, provided p = 0 and q = 0. By convention, it is generally agreed to call the zero vector orthogonal to every vector. Then we can conclude p ⊥ q if and only if p · q = 0, whether p or q is 0 or not. 4. (Orthogonality in Rn ). In Rn , for every n > 3, we deﬁne two vectors p and q to be orthogonal to each other if p · q = 0.

1. 5, B is a 3 × 4 matrix. Similarly, if a matrix has m rows and n columns, we call it an m × n matrix. In describing matrices, we always say rows ﬁrst, then columns. The general form of an m × n matrix is ⎡ ⎤ a11 a12 · · · a1n ⎢ a21 a22 · · · a2n ⎥ ⎢ ⎥ A=⎢ . 9) .. ⎥ , ⎣ .. . ⎦ am1 am2 · · · amn where the a11 , a12 , . . ) are arbitrary real numbers. They are called the entries of the matrix A, with aij denoting the entry at the intersection of the ith row and jth column. Thus in the double subscript ij the order is important.

Find the angles between its various edges, and try to draw it. 8. Consider a triangle in the xy plane with vertices A = (1, 3), B = (2, 4), and C = (4, −1). Find −−→ −−→ a. the orthogonal projection of p = AB onto the line of q = BC, b. the distance of A from that line, and c. 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.