April 2025
Intermediate to advanced
328 pages
8h 42m
Portuguese (Portugal, Brazil)
Content preview from Álgebra linear prática para a ciência dos dados
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Capítulo 7. Aplicações matriciais
Este trabalho foi traduzido com recurso a IA. Agradecemos o teu feedback e comentários: translation-feedback@oreilly.com
Espero que agora, depois dos últimos dois capítulos com muita teoria, te sintas como se tivesses acabado de fazer um treino intenso no ginásio: exausto mas com energia. Este capítulo deve parecer-te um passeio de bicicleta pelas colinas do campo: por vezes, um esforço, mas com uma perspetiva nova e inspiradora.
As aplicações deste capítulo são construídas a partir das do Capítulo 4. Fiz isto para ter alguns fios comuns que ligam os capítulos sobre vectores e sobre matrizes. E porque quero que vejas que, embora os conceitos e as aplicações se tornem mais complexos à medida que progrides na álgebra linear, as bases continuam a assentar nos mesmos princípios simples, como as combinações lineares ponderadas e o produto escalar.
Matrizes de covariância de dados multivariados
No Capítulo 4, aprendeste a calcular o coeficiente de correlação de Pearson como o produto escalar do vetor entre duas variáveis de dados, dividido pelo produto das normas do vetor. Essa fórmula era para duas variáveis (por exemplo, altura e peso); e se tiveres múltiplas variáveis (por exemplo, altura, peso, idade, exercício semanal...)?
Podias imaginar escrever um duplo for loop sobre todas as variáveis e aplicar a fórmula de correlação bivariada a todos os pares de variáveis. Mas isso é complicado e deselegante e, portanto, antitético ao espírito da álgebra ...
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