2.3 - Section 2.3 "Special Matrices", Powers &...

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Section 2.3 "Special Matrices", Powers & Non-Properties Definition of the Identity Matrix-- The identity matrix is a square matrix where the entries in the main diagonal are 1's and all other entries are 0's. Notation: I n is the n X n identity matrix. Examples 2 10 01 I = 3 100 010 001 I = 4 1000 0100 0010 0001 I   = 
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Property of the Identity Matrix: If A is an m X n matrix then I m A = A A I n = A Example 123 456 A  =   2 I A = 10123 01 = 3 AI = 100 010 001 = Definition of the Zero Matrix-- Every entry in the zero matrix is a 0. It can be any size (it does not have to be square). Notation: 0 mn is the m X n zero matrix.
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Examples: 23 000 0 = 31 0 00 0 = Properties of the Zero Matrix: If A is an mXn matrix, then A + 0 mn = A 0 mn + A = A A 0 np = 0 mp 0 pm A = 0 pn Examples 12 34  +   =
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12 34 000 56000 78    = Note: Watch the dimensions!
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This note was uploaded on 10/16/2009 for the course MATH 1114 at Virginia Tech.

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2.3 - Section 2.3 "Special Matrices", Powers &...

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