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Note_04M.36-40

# Note_04M.36-40 - 36 Portfolio Frontier of Many Assets When...

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36 Portfolio Frontier of Many Assets When there are more than two assets, it is extremely tedious to derive and express the portfolio possibility curve by the methods described above. It is much more convenient to use linear algebra to do this. It requires only a minimum amount of linear algebra. _______________________________________________________ Definition: Column vector, row vector, and matrix 3×1 column vector 1×4 row vector 2×3 matrix Definition. Transpose of a matrix Transpose of a 3×1 column vector a is a 1×3 row vector and denoted by a N : Transpose of the 2×3 matrix C is a 3×2 matrix Definition: Multiplication of matrices. Let matrices A and B are defined as Then, the multiplication AB is defined as a 2×2 matrix Note that the number of columns of A must be the same as the number of rows of B for proper multiplication (conformable for multiplication).

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37 Definition. An inverse of a non-singular square matrix V , denoted by , is a matrix such that , where I is an identity matrix whose diagonal elements are 1 and off-diagonal elements are zeros: Matrix V must be a square non-singular matrix.
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Note_04M.36-40 - 36 Portfolio Frontier of Many Assets When...

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