lec1_5

# lec1_5 - NOTES ON SECTION 1.5 MA265, SECTIONS 41, 52 Key...

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NOTES ON SECTION 1 . 5 MA265, SECTIONS 41, 52 Key words Diagonal matrix Symmetric matrix Nonsingular matrix (Invertible) Identity matrix Skew symmetric matrix Inverse Powers of a matrix Submatrix Upper triangular Partioned matrix Lower triangular matrix 1. Special types of matrices and partioned matrices Deﬁnition 1. A diagonal matrix is a square matrix where the only non-zero terms occur at entries a i i (these entries are called the main diagonal ). Example 2. Some examples of diagonal matrices: 2 0 0 0 0 - 1 0 0 0 0 4 0 0 0 0 - 3 , 2 0 0 0 - 1 0 0 0 π , π 0 0 0 2 0 0 0 0 , 0 0 0 0 0 0 0 0 1 , ± 2 0 0 - 1 ² , Deﬁnition 3. The n × n identity matrix is the unique square matrix of size n × n such that each entry on the main diagonal is a 1 . Example 4. The 3 × 3 identity matrix is 1 0 0 0 1 0 0 0 1 Deﬁnition 5. A matrix A is symmetric if A = A T . A matrix is skew-symmetric if A T = - A . We won’t really use skew-symmetric matrices much, but symmetric matrices come up often and their

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## This note was uploaded on 03/31/2012 for the course MA 265 taught by Professor Bens during the Spring '08 term at Purdue.

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lec1_5 - NOTES ON SECTION 1.5 MA265, SECTIONS 41, 52 Key...

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