eistein notation (h.1)...2016/06/08  · nth column of matrix a becomes a m n. we can then write the...

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Copyright (c) 2016 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Eistein Notation (H.1) 20160608

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Page 1: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also

Copyright (c) 2016 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of theGNU Free Documentation License, Version 1.2 or any later version published by the Free SoftwareFoundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy ofthe license is included in the section entitled "GNU Free Documentation License".

Eistein Notation (H.1)

20160608

Page 2: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 3: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 4: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 5: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 6: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 7: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 8: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 9: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 10: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 11: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 12: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 13: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 14: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 15: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 16: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 17: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 18: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 19: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 20: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 21: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 22: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 23: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 24: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 25: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 26: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 27: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 28: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 29: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 30: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 31: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 32: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also

A set is a collection of unique elements. The definition of a specific set determines which elements are members of the set. Elements not specifically defined as members of a set are not in the set.

A group is an algebraic system consisting of a set, an identity element, one operation and its inverse operation.

A ring is an algebraic system consisting of a set, an identity element, two operations and the inverse operation of the first operation.

A field is an algebraic system consisting of a set, an identity element for each operation, two operations and their respective inverse operations.

http://www.csee.umbc.edu/portal/help/theory/group_def.shtml

Page 33: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 34: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 35: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 36: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 37: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 38: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 39: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 40: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 41: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 42: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 43: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 44: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 45: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 46: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 47: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 48: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also
Page 49: Eistein Notation (H.1)...2016/06/08  · nth column of matrix A becomes A m n. We can then write the following operations in Einstein notation as follows. Inner product (hence also