ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED)

EE210A: Adaptation and Learning Professor Ali H. Sayed

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 2

MAIN RESULT FROM LAST LECTURE

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 3

MAIN RESULT FROM LAST LECTURE

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LECTURE #02

VECTOR AND COMPLEX-VALUED MEAN-SQUARE ERROR ESTIMATION Sections in order: B.1, A.3, A.4, 2.1, 2.2, 2.3

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 5

HERMITIAN MATRICES

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SPECTRAL DECOMPOSITION

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POSITIVE-DEFINITE MATRICES

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POSITIVE-DEFINITE MATRICES

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COMPLEX VARIABLES

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ORTHOGONAL RANDOM VARIABLES

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 11

EXAMPLE

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VECTOR-VALUED RANDOM VARIABLES

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 13

EXAMPLE

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PROPERTIES OF COVARIANCE MATRICES

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 15

ESTIMATING A SCALAR FROM A VECTOR

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 16

EXAMPLE

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EXAMPLE

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ESTIMATING A VECTOR FROM A VECTOR

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EQUIVALENT CRITERION

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 20

EQUIVALENT CRITERION

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OPTIMAL ESTIMATOR

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GAUSSIAN VARIABLES

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VECTOR GAUSSIAN VARIABLES

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CIRCULARITY ASSUMPTIONS

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CIRCULAR GAUSSIAN VARIABLES

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 26

ESTIMATION WITH GAUSSIAN DATA

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TRIANGULAR FACTORIZATION

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AFFINE RELATION

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ZERO MEAN CASE

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EQUIVALENT CRITERION

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 31

EQUIVALENT CRITERION

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EQUIVALENT CRITERION

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EQUIVALENT CRITERION

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EQUIVALENT CRITERION

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COMPUTER PROJECT

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COMPUTER PROJECT

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COMPUTER PROJECT SOLUTION

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COMPUTER PROJECT SOLUTION