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°³Á¤ÆÇ ¸Ó¸®¸»
Á¦1Àå Çà·Ä°ú Gauss ¼Ò°Å¹ý
1.1. Matrix
1.2. Gaussian Elimination
1.3. Elementary Matrix
1.4. Equivalence Class¿Í Partition
Á¦2Àå º¤ÅÍ°ø°£
2.1. Vector Space
2.2. Subspace
2.3. Vector SpaceÀÇ º¸±â
2.4. Isomorphism
Á¦3Àå ±âÀú¿Í Â÷¿ø
3.1. Linear Combination
3.2. ÀÏÂ÷µ¶¸³°ú ÀÏÂ÷Á¾¼Ó
3.3. Vector SpaceÀÇ Basis
3.4. BasisÀÇ Á¸Àç
3.5. Vector SpaceÀÇ Dimension
3.6. ¿ì¸®ÀÇ Ã¶ÇÐ
3.7. DimensionÀÇ º¸±â
3.8. Row-reduced Echelon Form
Á¦4Àå ¼±Çü»ç»ó
4.1. Linear Map
4.2. Linear MapÀÇ º¸±â
4.3. Linear Extension Theorem
4.4. Dimension Theorem
4.5. Rank Theorem
Á¦5Àå ±âº»Á¤¸®
5.1. Vector Space of Linear Maps
5.2. ±âº»Á¤¸®: Ç¥ÁرâÀúÀÇ °æ¿ì
5.3. ±âº»Á¤¸®: ÀϹÝÀûÀÎ °æ¿ì
5.4. ±âº»Á¤¸®ÀÇ °á°ú¿Í ¿ì¸®ÀÇ Ã¶ÇÐ
5.5. Change of Bases
5.6. Similarity Relation
Á¦6Àå Çà·Ä½Ä
6.1. Alternating Multilinear Form
6.2. Symmetric Group
6.3. DeterminantÀÇ Á¤ÀÇ I
6.4. DeterminantÀÇ ¼ºÁú
6.5. DeterminantÀÇ Á¤ÀÇ II
6.6. Cramer¡¯s Rule
6.7. Adjoin...t Matrix
Á¦7Àå Ư¼º´ÙÇ׽İú ´ë°¢È
7.1. Eigen-vector¿Í Eigen-value
7.2. Diagonalization
7.3. Triangularization
7.4. Cayley-Hamilton Theorem
7.5. Minimal Polynomial
7.6. Direct Sum°ú Eigen-space
Decomposition
Á¦8Àå ºÐÇØÁ¤¸®
8.1. Polynomial
8.2. T-Invariant Subspace
8.3. Primary Decomposition Theorem
8.4. Diagonalizability
8.5. T-Cyclic Subspace
8.6. Cyclic Decomposition Theorem
8.7. Jordan Canonical Form
Á¦9Àå RnÀÇ Rigid Motion 241
9.1. Rn-°ø°£ÀÇ Dot Product
9.2. Rn-°ø°£ÀÇ Rigid Motion
9.3. Orthogonal Operator / Matrix
9.4. Reflection
9.5. O(2)¿Í SO(2)
9.6. SO(3)¿Í SO(n)
Á¦10Àå ³»Àû °ø°£
10.1. Inner Product Space
10.2. Inner Product SpaceÀÇ ¼ºÁú
10.3. Gram-Schmidt Orthogonalization
10.4. Standard Basis Óß Orthonormal Basis
10.5. Inner Product SpaceÀÇ Isomorphism
10.6. Orthogonal Group°ú Unitary Group
10.7. Adjoint Matrix¿Í ±× ÀÀ¿ë
Á¦11Àå ±º
11.1. Binary Operation°ú Group
11.2. GroupÀÇ Ãʺ¸Àû ¼ºÁú
11.3. Subgroup
11.4. ÇкΠ´ë¼öÇÐÀÇ Úâ
11.5. Group Isomorphism
11.6. Group Homomorphism
11.7. Cyclic Group
11.8. Group°ú HomomorphismÀÇ º¸±â
11.9. Linear Group
Á¦12Àå Quotient
12.1. Coset
12.2. Normal Subgroup°ú Quotient Group
12.3. Quotient Space
12.4. Isomorphism Theorem
12.5. Triangularization II
Á¦13Àå Bilinear Form
13.1. Bilinear Form
13.2. Quadratic Form
13.3. Orthogonal Group°ú Symplectic Group
13.4. O(1, 1)°ú O(3, 1)
13.5. Non-degenerate Bilinear Form
13.6. Dual Space¿Í Dual Map
13.7. Duality
13.8. B-Identification
13.9. Transpose Operator
Á¦14Àå Hermitian Form
14.1. Hermitian Form
14.2. Non-degenerate Hermitian Form
14.3. H-Identification°ú Adjoint Operator
Á¦15Àå Spectral Theorem
15.1. Ç¥±â¹ý°ú ¿ë¾î
15.2. Normal Operator
15.3. Symmetric Operator
15.4. Orthogonal Operator
15.5. Epilogue
Á¦16Àå Topology ¸Àº¸±â
16.1. Matrix Group Isomorphism
16.2. Compactness¿Í Connectedness
Âü°í ¹®Çå
Ç¥±â¹ý ã¾Æº¸±â
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¼¿ï´ëÇб³ ¼öÇаú Á¹¾÷ Yale University Ph. D.
[Àú¼] ¼±Çü´ë¼ö¿Í ±º(°³Á¤ÆÇ)(¼¿ï´ëÃâÆǹ®È¿ø, 2015.05.15) ´ë¼öÇÐ(¼¿ï´ëÃâÆǹ®È¿ø, 2014.02.05) ¼±Çü´ë¼ö¿Í ±º(¼¿ï´ëÃâÆǹ®È¿ø, 2014.02.15) ¿Ü ´Ù¼ö
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