Linear Algebra and Projective Geometry

Β· Courier Corporation
αžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž…
336
αž‘αŸ†αž–αŸαžš
αž€αžΆαžšαžœαžΆαž™αžαž˜αŸ’αž›αŸƒ αž“αž·αž„αž˜αžαž·αžœαžΆαž™αžαž˜αŸ’αž›αŸƒαž˜αž·αž“αžαŸ’αžšαžΌαžœαž”αžΆαž“αž•αŸ’αž‘αŸ€αž„αž•αŸ’αž‘αžΆαžαŸ‹αž‘αŸ αžŸαŸ’αžœαŸ‚αž„αž™αž›αŸ‹αž”αž“αŸ’αžαŸ‚αž˜

αž’αŸ†αž–αžΈαžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αž“αŸαŸ‡

Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebraic structures such as the endomorphism ring of the underlying manifold or the full linear group.
Restricted to topics of an algebraic nature, the text shows how far purely algebraic methods may extend. It assumes only a familiarity with the basic concepts and terms of algebra. The methods of transfinite set theory frequently recur, and for readers unfamiliar with this theory, the concepts and principles appear in a special appendix.

αžœαžΆαž™αžαž˜αŸ’αž›αŸƒαžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αž“αŸαŸ‡

αž”αŸ’αžšαžΆαž”αŸ‹αž™αžΎαž„αž’αŸ†αž–αžΈαž€αžΆαžšαž™αž›αŸ‹αžƒαžΎαž‰αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ”

αž’αžΆαž“β€‹αž–αŸαžαŸŒαž˜αžΆαž“

αž‘αžΌαžšαžŸαž–αŸ’αž‘αž†αŸ’αž›αžΆαžαžœαŸƒ αž“αž·αž„β€‹αžαŸαž”αŸ’αž›αŸαž
αžŠαŸ†αž‘αžΎαž„αž€αž˜αŸ’αž˜αžœαž·αž’αžΈ Google Play Books αžŸαž˜αŸ’αžšαžΆαž”αŸ‹ Android αž“αž·αž„ iPad/iPhone αŸ” αžœαžΆβ€‹αž’αŸ’αžœαžΎαžŸαž˜αž€αžΆαž›αž€αž˜αŸ’αž˜β€‹αžŠαŸ„αž™αžŸαŸ’αžœαŸαž™αž”αŸ’αžšαžœαžαŸ’αžαž·αž‡αžΆαž˜αž½αž™β€‹αž‚αžŽαž“αžΈβ€‹αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€β€‹ αž“αž·αž„β€‹αž’αž“αž»αž‰αŸ’αž‰αžΆαžαž±αŸ’αž™β€‹αž’αŸ’αž“αž€αž’αžΆαž“αž–αŸαž›β€‹αž˜αžΆαž“αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αž αž¬αž‚αŸ’αž˜αžΆαž“β€‹αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αžβ€‹αž“αŸ…αž‚αŸ’αžšαž”αŸ‹αž‘αžΈαž€αž“αŸ’αž›αŸ‚αž„αŸ”
αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžšβ€‹αž™αž½αžšαžŠαŸƒ αž“αž·αž„αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžš
αž’αŸ’αž“αž€αž’αžΆαž…αžŸαŸ’αžŠαžΆαž”αŸ‹αžŸαŸ€αžœαž—αŸ…αž‡αžΆαžŸαŸ†αž‘αŸαž„αžŠαŸ‚αž›αž”αžΆαž“αž‘αž·αž‰αž“αŸ…αž€αŸ’αž“αž»αž„ Google Play αžŠαŸ„αž™αž”αŸ’αžšαžΎαž€αž˜αŸ’αž˜αžœαž·αž’αžΈαžšαž»αž€αžšαž€αžαžΆαž˜αž’αŸŠαžΈαž“αž’αžΊαžŽαž·αžαž€αŸ’αž“αž»αž„αž€αž»αŸ†αž–αŸ’αž™αžΌαž‘αŸαžšαžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ”
eReaders αž“αž·αž„β€‹αž§αž”αž€αžšαžŽαŸβ€‹αž•αŸ’αžŸαŸαž„β€‹αž‘αŸ€αž
αžŠαžΎαž˜αŸ’αž”αžΈαž’αžΆαž“αž“αŸ…αž›αžΎβ€‹αž§αž”αž€αžšαžŽαŸ e-ink αžŠαžΌαž…αž‡αžΆβ€‹αž§αž”αž€αžšαžŽαŸαž’αžΆαž“β€‹αžŸαŸ€αžœαž—αŸ…αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€ Kobo αž’αŸ’αž“αž€αž“αžΉαž„αžαŸ’αžšαžΌαžœβ€‹αž‘αžΆαž‰αž™αž€β€‹αž―αž€αžŸαžΆαžš αž αžΎαž™β€‹αž•αŸ’αž‘αŸαžšαžœαžΆαž‘αŸ…β€‹αž§αž”αž€αžšαžŽαŸβ€‹αžšαž”αžŸαŸ‹αž’αŸ’αž“αž€αŸ” αžŸαžΌαž˜αž’αž“αž»αžœαžαŸ’αžαžαžΆαž˜β€‹αž€αžΆαžšαžŽαŸ‚αž“αžΆαŸ†αž›αž˜αŸ’αž’αž·αžαžšαž”αžŸαŸ‹αž˜αž‡αŸ’αžˆαž˜αžŽαŸ’αžŒαž›αž‡αŸ†αž“αž½αž™ αžŠαžΎαž˜αŸ’αž”αžΈαž•αŸ’αž‘αŸαžšαž―αž€αžŸαžΆαžšβ€‹αž‘αŸ…αž§αž”αž€αžšαžŽαŸαž’αžΆαž“αžŸαŸ€αžœαž—αŸ…β€‹αž’αŸαž‘αž·αž…αžαŸ’αžšαžΌαž“αž·αž€αžŠαŸ‚αž›αžŸαŸ’αž‚αžΆαž›αŸ‹αŸ”