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Page 1: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

Course 395: Machine Learning – Math. Intro.

Brief Intro to Matrices, Vectors and Derivatives:

•Equality: Two matrices and are equal iff

•Matrix addition

• Scalar Multilplication

Page 2: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

Neural Networks – Math. Intro.

•Matrix transposition:

•Dot product:

Page 3: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

•Matrix Multiplication: Let two matrices and then : the dot product of the i-th row of and the j-th column of

•Example:

Neural Networks – Math. Intro.

Page 4: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

•Partial derivatives Example 1:

Neural Networks – Math. Intro.

Page 5: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

•Example 2:

Neural Networks – Math. Intro.

Page 6: Stefanos Zafeiriou Machine Learning(395) Course 395: Machine Learning – Math. Intro. Brief Intro to Matrices, Vectors and Derivatives: Equality: Two matrices

Stefanos Zafeiriou Machine Learning(395)

•Optimization problem

Compute the partial derivatives

Neural Networks – Math. Intro.


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