Linear algebra. Lecture 3

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Linear algebra
Lecture 3
Matrix Algebra
2.1 Matrix Operations;
2.2 The Inverse of a Matrix;
2.3 Characterizations of Invertible Matrices;
2.4 Partitioned Matrices
2.5 Matrix Factorizations

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Learning Objectives:
1. The meaning and characterizations of invertible matrix.
2. Finding the LU factorization of the matrix.
3. Sum and scalar multiples.
4. Properties of matrix.

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2.2 The Inverse of a Matrix.

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An Algorithm for Finding A-1

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2.3. Characterizations of Invertible Matrices.

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2.4. Partitioned Matrices.
A block matrix or a partitioned matrix is a partition of a matrix into rectangular
smaller matrices called blocks.

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2.5. Matrix Factorizations.
A factorization of a matrix A is an equation that expresses A as a product of two
or more matrices.
The LU Factorization
Ly=b
Ux=y

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