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第02号 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/11178/2888

Title: 線形代数の教材について : 平行性を用いた2次の行列式および2次元ベクトルの内積の幾何学的構成
Other Titles: On Teaching Materials of the Linear Algebra : Geometric constructipns of determinants of order two and inner products of two dimensional vectors by using parallelism
Authors: 渋谷, 謙一
山口, 清
SHIBUYA, Ken-ichi
YAMAGUTI, Kiyosi
シブヤ, ケンイチ
ヤマグチ, キヨシ
九州産業大学国際文化学部 / 九州産業大学国際文化学部
THE SOCIENTY OF THE FACULTY OF INTERNATIONAL STUDIES OF CULTURE KYUSYU SANGYO UNIVERSITY / THE SOCIENTY OF THE FACULTY OF INTERNATIONAL STUDIES OF CULTURE KYUSYU SANGYO UNIVERSITY
Issue Date: Mar-1995
Publisher: 九州産業大学国際文化学会
Abstract: This is a case study of teaching materials of the linear algebra. The linear algebra can be understood from two points of view, that is, algebraic and geometric. Here, we consider two elementary topics of the linear algebra; the determinants of order two and the inner products of two dimensional number vectors. The purpose of this paper is to study the geometric constructions of these objects. A parallelism is used for these constructions, more precisely, we use the segments calculation by D. Hilbert and a parallel projection along the line y = mx with slope m of a point to the x-axis or the y-axis. The determinant and inner product are constructed corresponding to the slope m = 1 and -1 respectively, since the determinant is alternative with respect to its columns and the inner product is symmetric bilinear form. As an application of the construction by using parallelism, we consider geometric constructions of the solution of the system of linear equations. It seems that the geometric construction by using parallelism is effective for intuitive understanding of the teaching materials stated above.
URI: http://hdl.handle.net/11178/2888
Appears in Collections:第02号

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