2. Matrix Algebra

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2. Matrix Algebra

• 2.1 Matrix Operations

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j-th column
i-th row
Diagonal entries
Diagonal matrix a square matrix whose
nondiagonal entries are zero.
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Recall Two matrices are the same
the matrices are the same size and their
corresponding entries are equal.
Theorem 1 Let A, B, and C be matrices of the
same size, and let r and s be scalars.
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Example
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Example
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REVIEW
Matrix Multiplication
Recall
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Matrix Multiplication
Example Let
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Row-Column Rule for Computing AB If the product
AB is defined, then the entry in row i and column
j of AB is the sum of the products of
corresponding entries from row i of A and column
j of B.
Example
3x2
2x2
3x2
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Properties of Matrix Multiplication


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Defn Given an mxn matrix A, the transpose of A
is the nxm matrix, denoted by AT, whose columns
are formed from the corresponding rows of A.
Example Let
What is AT ?
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Rules related to transpose