Lectures related to Mechanobiology of Biofilms

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Matrix Operations: Composition and Product

Covers the composition and product of matrices, including matrix multiplication.

Matrix Operations: Coefficients, Combinations, and Applications

Covers matrix operations, coefficients, combinations, and applications in various scenarios.

Linear Algebra: Matrices and Operations

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Extracellular Matrix and Cell Communication

Explores the extracellular matrix, cell-ECM interactions, and bacterial systems.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Linear Algebra: Matrices and Inverses

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Linear Transformations: Injective and Surjective

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Matrix Operations: Transposition, Rank, and Basis Change

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Matrix Properties

Explores matrix shapes, compatibility, and invertibility, including staggered shapes and system compatibility.

Determinants and Properties

Covers the definition and properties of determinants, including the rule of Sarrus for 3x3 matrices.

Matrix Form and IO Analysis

Covers Material Flow Analysis in matrix form and Input-Output Analysis, exploring balance equations, transfer coefficients, GHG emissions, and economic impact.

Matrix Operations: Product and Inverse

Covers matrix operations, focusing on the product and inverse of matrices.

Matrix Operations: Definitions and Examples

Covers the basic operations on matrices, including addition, scalar multiplication, and matrix multiplication.

Projections and Applications

Explores projections in R³, matrix properties, and trace concepts with practical examples.