Fundamentos de Álgebra Lineal from edX

Nuestro curso de álgebra lineal te propone acercarte a los fundamentos de esta importante materia para comprender las bases que te permitirán entrar a las aplicaciones más actuales de este tema.

El curso tiene un enfoque en dos vertientes centrales, queremos que aprendas a entrar a las bases más profundas del álgebra lineal, al tiempo que seas capaz de vincularlas a las aplicaciones prácticas. Para lograrlo, hemos organizado el contenido de manera que al mismo tiempo que entremos en una reflexión sobre los aspectos teóricos claves, también utilicemos software actual para comprender las aplicaciones más utilizadas; nuestro curso te presentará a lo largo de 6 semanas la posibilidad de entender el mundo de los sistemas de ecuaciones, su relación con los vectores y su resolución completa.

What's inside

Learning objectives

Distinguir la relación de los sistemas de ecuaciones con los vectores y las matrices.
Resolver cualquier sistema de ecuaciones y dar la solución más cercana a aquellos que no la tengan.

Comprender la relación entre los sistemas de ecuaciones y los cuatro subespacios fundamentales del álgebra lineal.

Distinguir la relación de los sistemas de ecuaciones con los vectores y las matrices.
Resolver cualquier sistema de ecuaciones y dar la solución más cercana a aquellos que no la tengan.
Comprender la relación entre los sistemas de ecuaciones y los cuatro subespacios fundamentales del álgebra lineal.

Syllabus

Semana 1. Introducción

Explicación de la modalidad de trabajo en la plataforma

0.1 0.1.1 Bienvenida al curso

0.1.2 Temas a abordar

0.1.3 Lo que se aprenderá

0.1.4 Recursos necesarios

0.2 0.2.1 Introducción a la plataforma

0.2.2 Modo de trabajo

0.2.3 Modo de evaluación

Introducción a Vectores

Introducción al concepto de vectores y sus aplicaciones en la materia

1.1 Introducción

1.1.2 Que se aprenderá

1.2 1.2.1 Qué es un vector

1.2.2 Graficación de un vector

1.3 1.3.1 Qué es una combinación lineal

1.3.2 El secreto del Álgebra Lineal

1.3.3 Ejercicios

1.4 1.4.1 Representación perspectiva de columna y fila

1.4.2 Ejercicios

1.5 1.5.1 Video de experto

1.6 1.6.1 Resumen del capítulo

1.6.2 Reflexión final

1.7 Evaluación

Semana 2. Matrices y sistemas de ecuaciones

Solución de sistemas de ecuaciones

2.1 2.1.1 Introducción al capítulo

2.1.2 Que se aprenderá

2.2 2.2.1 Qué es una matriz

2.2.2 Relación de los sistemas de ecuaciones con las matrices

2.2.3 Ejercicios

2.3 2.3.1 Identificar si los términos son multiplicables

2.3.2 Multiplicación de matriz por vector

2.3.3 Multiplicación de matriz por matriz

2.3.4 Ejercicios

2.4 2.4.1 Identificación de pivotes

2.4.2 Método de Gauss

2.4.3 Casos especiales

2.4.4 Ejercicios

2.5 Video de experto

2.6 2.6.1 Resumen del capítulo

2.6.2 Reflexión final

2.7 Evaluación

Semana 3. Matriz inversa

Solucionar sistemas de ecuaciones encontrando la inversa de una matriz

3.1 3.1.1 Introducción al capítulo

3.1.2 Que se aprenderá

3.2 3.2.1 Sistemas invertibles

3.2.2 Matriz inversa

3.3 3.3.1 Independencia lineal

3.3.2 Ejercicios

3.4 3.4.1 Cálculo de inversa mediante Gauss Jordan

3.4.2 Ejercicios

3.5 Aplicaciones

3.6 3.6.1 Resumen del capítulo

3.6.2 Reflexión final

3.7 Evaluación

Semana 4. Espacios vectoriales

Análisis de los cuatro espacios fundamentales del álgebra lineal

4.1 4.1.1 Introducción al capítulo

4.1.2 Que se aprenderá

4.2 4.2.1 Qué es un espacio y subespacio

4.3 4.3.1 Que es el subespacio de columna

4.3.2 Determinación del subespacio de columna

4.3.3 Determinación de las características

4.3.4 Ejercicios

4.4 4.4.1 Qué es el subespacio nulo

4.4.2 Determinación del subespacio nulo

4.4.3 Determinación de las características

4.4.4 Ejercicios

4.5 4.5.1 Solución completa

4.5.2 Determinación de la solución completa

4.5.3 Ejercicios

4.6 4.6.1 Qué son los espacios traspuestos

4.6.2 Características de los espacios traspuestos

4.6.3 Ejercicios

4.7 Aplicaciones

4.8 4.8.1 Resumen del capítulo

4.8.2 Reflexión final

4.9 Evaluación

Semana 5. Ortogonalidad y proyecciones

Ortogonalidad entre espacios y proyección de vectores

5.1 5.1.1 Introducción al capítulo

5.1.2 Que se aprenderá

5.2 5.2.1 Ortogonalidad entre vectores

5.2.2 Demostraciones

5.2.3 Ejercicios

5.3 5.3.1 Ortogonalidad entre subespacios

5.3.2 Ejercicios

5.4 5.4.1 La idea de proyecciones

5.4.2 Cálculo de proyecciones

5.4.3 Ejercicios

5.5 Aplicaciones

5.6 5.6.1 Resumen del capítulo

5.6.2 Reflexión final

5.7 Evaluación

Semana 6. Eigenvectores

6.1 6.1.1 Introducción al capítulo

6.1.2 Que se aprenderá

6.2 6.2.1 Concepto de eigenvector y eigen valor

6.3 6.3.1 Cálculo de eigenvectores y eigenvalores

6.3.2 Ejercicios

6.4 6.4.1 La lógica de los eigenvalores

6.5 6.5.1 Diagonalización

6.6 6.6.1 Aplicaciones

6.7 6.7.1 Resumen del capítulo

6.7.2 Reflexión final

6.8 Evaluación

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Enseña los fundamentos esenciales del álgebra lineal

Aborda tanto las bases teóricas como las aplicaciones prácticas

Utiliza software actual para comprender las aplicaciones más utilizadas

Cubre una amplia gama de temas, desde vectores y sistemas de ecuaciones hasta espacios vectoriales y eigenvectores

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Fundamentos de Álgebra Lineal with these activities:

Go to Khan Academy to Review Vectors

Show steps

This course involves working with vectors. A review of the concepts of vectors will help you to succeed in this course.

Browse courses on Vectors

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Visit the Khan Academy website.
Search for 'Vectors'.
Watch the videos and complete the exercises.

Solve Systems of Equations Practice Problems

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Gain proficiency in solving systems of equations by completing practice problems.

Browse courses on Systems of Equations

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Find practice problems online or in a textbook.
Solve the problems, checking your answers.

Matrix Operations Cheat Sheet

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Create a quick reference guide to matrix operations.

Browse courses on Matrices

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Gather information on matrix operations.
Organize the information into a concise cheat sheet.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Study Group for Algebra Linear

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Enhance your understanding by participating in a study group.

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Find a study group or form one with classmates.
Meet regularly to discuss course material and solve problems together.
Quiz each other to test your understanding.

Volunteer at a Math Club

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Deepen your understanding of algebra by volunteering at a math club.

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Find a math club in your area.
Contact the club and inquire about volunteering opportunities.
Attend club meetings and assist with math activities.

Eigenvectors and Eigenvalues Crash Course

Show steps

Gain insight into eigenvectors and eigenvalues by exploring guided tutorials.

Browse courses on Eigenvectors and Eigenvalues

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Search for 'Eigenvectors and Eigenvalues Crash Course' on YouTube.
Watch the videos and take notes.

Linear Algebra and Its Applications

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Expand your knowledge of linear algebra by reading a comprehensive textbook.

View Álgebra Lineal Y Sus Aplicaciones on Amazon

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Obtain a copy of the book.
Read the chapters relevant to the course.
Complete the practice problems at the end of each chapter.

Career center

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